Publications
Publications by Anthony W. Knapp
Below is a list of my publications---books, articles, and other writing. In
some cases links are provided to places on the web where an abstract, preprint,
or reprint of the article may be found.
Skip to: 1964 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | Book reviews | Notices essays | Other items.
Books and articles
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Distal functions, Proceedings of the National
Academy of Sciences of the USA 52 (1964), 1409-1412.
Reprint in PDF.
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Connection between Brownian motion and potential
theory, Journal of Mathematical Analysis and Applications
12 (1965), 328-349.
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Regular boundary points in Markov chains,
Proceedings of the American Mathematical Society 17 (1966), 435-440.
Link to
journal.
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(with J. G. Kemeny and J. L. Snell)
Denumerable Markov Chains,
D. Van Nostrand Co., Inc., Princeton, New Jersey, 1966.
Access to the table of contents
and the preface.
-
Decomposition theorem for bounded uniformly continuous
functions
on a group, American Journal of Mathematics 88 (1966),
902-914.
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Distal functions on groups, Transactions of the
American Mathematical Society 128 (1967), 1-40.
Link to
journal.
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Fatou's theorem for symmetric spaces I, Annals of
Mathematics
88 (1968), 106-127.
Link to
journal.
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Doubly generated Fuchsian groups, Michigan
Mathematical Journal 15 (1968), 289-304.
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Functions behaving like almost automorphic functions,
Topological Dynamics, an International Symposium, J.
Auslander and W. Gottschalk (ed.), W. A. Benjamin Inc., New York, 1968,
pp. 299-317.
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(with P. J. Kahn) Equivariant maps onto minimal flows,
Mathematics Systems Theory 2 (1968), 319-324.
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(with E. M. Stein) Singular integrals and the principal
series,
Proceedings of the National Academy of Sciences of the USA
63 (1969), 281-284.
Reprint in PDF.
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(with E. M. Stein) The existence of complementary
series,
Problems in Analysis, a Symposium in
Honor of Salomon Bochner, R. C. Gunning (ed.), Princeton University Press,
Princeton, New Jersey, 1970, pp. 249-259.
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(with E. M. Stein) Singular integrals and the principal
series
II, Proceedings of the National Academy of Sciences of the
USA 66 (1970), 13-17.
Reprint in PDF.
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(with E. M. Stein) Intertwining operators for
semisimple groups,
Annals of Mathematics 93 (1971), 489-578.
Link to
journal.
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(with R. E. Williamson) Poisson integrals and
semisimple groups,
Journal d'Analyse Mathématique 24 (1971), 53-76.
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(with E. M. Stein) Irreducibility theorems for the
principal
series, Conference on Harmonic Analysis,
Lecture Notes in Mathematics 266 (1972),
Springer-Verlag, New York, pp. 197-214.
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Bounded symmetric domains and holomorphic discrete
series,
Symmetric Spaces, W. M. Boothby and G. L. Weiss
(eds.), Marcel
Dekker Inc., New York, 1972, pp. 211-246.
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(with K. Okamoto) Limits of holomorphic discrete series,
Journal of Functional Analysis 9 (1972), 375-409.
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Determination of intertwining operators,
Harmonic Analysis on Homogeneous Spaces, Proceedings of Symposia in Pure
Mathematics 26 (1973), American
Mathematical Society, Providence, Rhode Island, pp. 263-268.
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Commutativity of intertwining operators, Bulletin of
the American Mathematical Society 79 (1973), 1016-1018.
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(with R. Harvey) Positive (p,p) forms, Wirtinger's
inequality,
and currents,
Value Distribution Theory, Part A, R. O. Kujala and
A. L. Vitter (eds.), Marcel Dekker Inc., New York, 1974,
pp. 43-62.
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(with E. M. Stein) Singular integrals and the principal
series
III, Proceedings of the National Academy of Sciences of the
USA 71 (1974), 4622-4624.
Reprint in PDF.
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A Szegö kernel for discrete series,
Proceedings of the International Congress of Mathematicians, 1974, 2
(1975), Canadian Mathematical Congress, 99-104.
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Weyl group of a cuspidal parabolic, Annales
Scientifiques de l'Ecole Normale Supérieure 8 (1975), 275-294.
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(with E. M. Stein) Singular integrals and the principal
series
IV, Proceedings of the National Academy of Sciences of the
USA 72 (1975), 2459-2461.
Reprint in PDF.
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Commutativity of intertwining operators II,
Bulletin of the American Mathematical Society 82 (1976),
271-273.
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(with J. G. Kemeny and J. L. Snell)
Denumerable Markov Chains, second edition,
Springer-Verlag, New York, 1976.
Access to the table of contents and
the two prefaces.
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(with E. M. Stein) Intertwining operators for SL(n,R),
Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann,
E. H. Lieb, B. Simon, and A. S. Wightman (eds.), Princeton Series in Physics,
Princeton University Press, Princeton, New Jersey, 1976,
pp. 239-267.
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(with N. R. Wallach) Szegö kernels associated with
discrete
series, Inventiones
Mathematicae 34 (1976), 163-200, and
62 (1980), 341-346.
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(with G. Zuckerman) Classification of irreducible
tempered
representations of semisimple Lie groups, Proceedings of
the National Academy of Sciences of the USA 73 (1976),
2178-2180.
Reprint in PDF.
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(with G. Zuckerman) Classification theorems for
representations
of semisimple Lie groups,
Non-Commutative Harmonic Analysis, Lecture Notes in
Mathematics
587 (1977), Springer-Verlag, New York, pp. 138-159.
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Irreducible tempered representations, Lie Theories
and Their Applications, Proceedings of the 1977 Annual Seminar of
the Canadian Mathematical Congress, Queen's Papers in
Pure and Applied Mathematics, No. 48, Queen's University,
Kingston, Ontario, 1978, pp. 487-495.
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Representations of GL$_2(R)$ and GL$_2(C)$,
Automorphic Forms, Representations, and $L$-Functions,
Proceedings of Symposia in Pure Mathematics 33 (1979), Part 1, American
Mathematical Society, Providence, Rhode Island, pp. 87-91.
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(with G. Zuckerman) Normalizing factors, tempered
representations, and $L$-groups,
Automorphic Forms, Representations, and $L$-Functions,
Proceedings of Symposia in Pure Mathematics
33 (1979), Part 1, American Mathematical Society, Providence,
Rhode Island, pp. 93-105.
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(with E. M. Stein) Intertwining operators for semisimple
groups II, Inventiones Mathematicae 60 (1980), 9-84.
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(with G. Zuckerman) Multiplicity one fails for
$\frak p$-adic unitary
principal series, Hiroshima Mathematical Journal 10
(1980), 295-309.
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(with S. S. Gelbart) Irreducible constituents of
principal series
of SL$_n(k)$, Duke Mathematical Journal 48 (1981),
313-326.
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(with E. M. Stein) Some new intertwining operators for
semisimple
groups, Non Commutative Harmonic Analysis and Lie Groups,
Lecture Notes in Mathematics 880 (1981),
Springer-Verlag, New York, pp.
303-336.
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Letter to David Vogan, Langlands L-classes exist for SU(3,2) that contain
a mixture of unitary and nonunitary representations, October 19, 1982.
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(with S. S. Gelbart) $L$-indistinguishability and $R$
groups for
the special linear group, Advances in Mathematics 43
(1982),
101-121.
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(with B. Speh) Irreducible unitary representations of
$SU(2,2)$,
Journal of Functional Analysis 45 (1982), 41-73.
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(with B. Speh) Status of classification of irreducible
unitary
representations, Harmonic Analysis, Lecture Notes in
Mathematics
908 (1982), Springer-Verlag, New York, pp. 1-38.
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Commutativity of intertwining operators for semisimple
groups,
Compositio Mathematica 46 (1982), 33-84.
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(with G. J. Zuckerman) Classification of irreducible
tempered
representations of semisimple groups, Annals of
Mathematics 116 (1982), 389-501, and 119 (1984), 639.
Link to
journal.
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Representation Theory of Semisimple Groups, by
Examples,
preliminary edition, Université Paris VII, Paris, 1982.
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Minimal K-type formula, Non Commutative Harmonic
Analysis and Lie Groups, Lecture Notes in
Mathematics 1020 (1983), Springer-Verlag, New York, pp. 107-118.
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(with B. Speh) The role of basic cases in
classification: Theorems
about unitary representations applicable to SU(N,2),
Non Commutative Harmonic Analysis and Lie Groups,
Lecture Notes in Mathematics 1020 (1983), Springer-Verlag, New York, pp.
119-160.
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Unitary representations and basic cases, Lie Group
Representations I, Lecture Notes in
Mathematics 1024 (1983), Springer-Verlag, New York, pp. 77-98.
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Investigations of unitary representations of semisimple
Lie groups, Topics in Modern Harmonic Analysis I, Proceedings of a
Seminar Held in Torino and Milano May-June 1982, Istituto Nazionale di Alta
Matematica Francesco Severi, Rome, 1983, pp. 9-43.
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(with M. W. Baldoni Silva) Indefinite intertwining
operators,
Proceedings of the National Academy of Sciences of the USA
81 (1984), 1272-1275.
Reprint in PDF.
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Langlands classification and unitary dual of $SU(2,2)$,
Applications of Group Theory in Physics and Mathematical Physics,
M. Flato, P. Sally, and G. Zuckerman (eds.),
Lectures in Applied Mathematics 21 (1985), American Mathematical
Society, Providence, Rhode Island, pp. 209-217.
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Representation Theory of Semisimple Groups: An
Overview Based on Examples, Princeton Mathematical Series 36,
Princeton University
Press, Princeton, New Jersey, 1986.
Access to the table of contents,
the preface, and a list of corrections.
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(with M. W. Baldoni-Silva) Unitary representations
induced from
maximal parabolic subgroups, Journal of Functional
Analysis 69 (1986), 21-120.
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(with D. A. Vogan) Duality theorems in relative Lie
algebra
cohomology, duplicated notes, SUNY
Stony Brook and Massachusetts Institute of Technology, 1986.
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(with M. W. Baldoni-Silva) Indefinite intertwining
operators II,
Analisi Armonica, Spazi Simmetrici e Teoria della
Probabilità, Cortona 2-5 Luglio 1984, Symposia Mathematica 29
(1987), Istituto Nazionale di Alta
Matematica Francesco Severi, Rome, pp. 1-44.
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(with M. W. Baldoni-Silva) Irreducible unitary
representations
of some groups of real rank two,
Non-Commutative Harmonic Analysis and Lie Groups, Lecture
Notes in Mathematics 1243 (1987), Springer-Verlag, New York, pp. 15-36.
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(with M. W. Baldoni-Silva) Vogan's algorithm for
computing
composition series,
Non-Commutative Harmonic Analysis and Lie Groups, Lecture
Notes in Mathematics 1243 (1987), Springer-Verlag, New York, pp. 37-72.
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Lie Groups, Lie Algebras, and Cohomology,
Princeton Mathematical
Notes 34, Princeton University Press, Princeton, New Jersey,
1988.
Access to the table of contents,
the preface, and a list of corrections.
-
(with M. W. Baldoni-Silva) Intertwining operators and
unitary
representations I, Journal of Functional Analysis 82
(1989),
151-236.
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(with M. W. Baldoni-Silva) Intertwining operators and
unitary
representations II, Société
Mathématique de France, Astérisque
171-172 (1989), 131-162.
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(with M. W. Baldoni-Silva) A construction of unitary
representations in parabolic rank two,
Annali della Scuola Normale Superiore di Pisa 16 (1989), 579-601.
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CRM Summer School Course on Representations of Real
Reductive Groups, Publications CRM, Université de Montréal,
Montréal, 1990.
Access to the table of contents and
the preface.
-
Imbedding discrete series in $L^2(G/H)$, in N. V.
Pedersen (ed.),
Harmonic Analysis on Lie Groups (Sandbjerg Estate, August
26-30, 1991), Copenhagen University Mathematics Institute, Report Series
1991, No. 3, Copenhagen, 1991, 27-29.
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(with M. W. Baldoni-Silva) Intertwining operators into
$L^2(G/H)$,
Representation
Theory of Lie Groups and Lie
Algebras, Fuji-Kawaguchiko, Aug
31-Sep 3, 1990, T. Kawazoe, T. Oshima, and S. Sano (eds.), World Scientific,
Singapore, 1992, pp. 95-119.
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(with L. Barchini and R. Zierau) Intertwining operators
into
Dolbeault cohomology representations, Journal of
Functional Analysis 107 (1992), 302-341.
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Elliptic Curves, Princeton Mathematical Notes 40,
Princeton University Press, Princeton, New Jersey, 1992.
Access to the table of contents,
the preface, and lists of corrections.
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Introduction to representations in analytic cohomology,
The Penrose Transform and Analytic Cohomology in Representation
Theory, M. Eastwood, J. Wolf, and R. Zierau (eds.), Contemporary
Mathematics 154 (1993), American Mathematical Society, Providence, Rhode
Island, pp. 1-19.
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Local Langlands correspondence: the archimedean case,
Motives, Proceedings of Symposia in Pure Mathematics 55 (1994), Part 2,
American
Mathematical Society, Providence, Rhode Island, pp. 393-410.
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(with D. A. Vogan) Cohomological Induction and
Unitary Representations, Princeton Mathematical Series 45,
Princeton University Press, Princeton, New Jersey, 1995.
Access to the table of contents,
the preface, and a list of corrections.
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Group representations and harmonic analysis from Euler
to Langlands, Part I, Notices of the American Mathematical Society
43 (1996), 410-415.
Reprint in PDF.
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Group representations and harmonic analysis from Euler
to Langlands, Part II, Notices of the American Mathematical Society 43
(1996), 537-549.
Reprint in PDF.
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Lie Groups Beyond an Introduction,
Progress in Mathematics 140, Birkhäuser, Boston, 1996.
Reprinted with corrections, 2001.
Access to the corrected pages
appearing in the 2001 reprint.
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A quick proof of the classification of simple real Lie
algebras, Proceedings of the American Mathematical Society 124 (1996),
3257-3259.
Reprint in PDF.
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Exceptional unitary representations of semisimple Lie
groups, Representation Theory 1 (1997), 1-24.
Reprint in PDF.
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(editor with T. N. Bailey) Representation Theory
and Automorphic Forms; An Instructional Conference at the International Centre
for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure
Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island.
Access to the table of contents
and the foreword.
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Structure theory of semisimple Lie groups,
Representation Theory and Automorphic Forms; An Instructional Conference at the
International Centre for Mathematical Sciences, Edinburgh, 1996,
Proceedings of Symposia in Pure Mathematics 61 (1997),
American Mathematical Society, Providence, Rhode Island, pp. 1-27.
Reprint in PDF.
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Introduction to the Langlands program,
Representation Theory and Automorphic Forms; An Instructional Conference at the
International Centre for Mathematical Sciences, Edinburgh, 1996,
Proceedings of Symposia in Pure Mathematics61 (1997),
American Mathematical Society, Providence, Rhode Island, pp. 245-302.
Reprint in PDF.
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Theoretical aspects of the trace formula for $GL(2)$,
Representation Theory
and Automorphic Forms; An Instructional Conference at the International Centre
for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure
Mathematics 61 (1997), American Mathematical Society,
Providence, Rhode
Island, pp. 355-405.
Reprint in PDF.
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(with J. D. Rogawski) Applications of the trace
formula, Representation Theory
and Automorphic Forms; An Instructional Conference at the International Centre
for Mathematical Sciences, Edinburgh, 1996, Proceedings of Symposia in Pure
Mathematics 61 (1997), American Mathematical Society, Providence, Rhode Island,
pp. 413-431.
Reprint in PDF.
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Survey of irreducible unitary representations of
semisimple Lie groups, GROUP21: Physical Applications and
Mathematical Aspects of Geometry, Groups, and Algebras, Proceedings of the XXI
International Colloquium, vol. 1, World Scientific, Singapore, 1997, pp.
89-98.
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André Weil: A prologue,
Notices of the American Mathematical Society 46 (1999), 434-439.
Abstract |
Reprint in PDF.
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Anneli Lax's Research Mathematics,
Notices of the American Mathematical Society 47 (2000), 768.
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(with P. E. Trapa) Representations of semisimple Lie groups,
Representation Theory of Lie Groups , J. Adams and D. Vogan (eds.),
IAS/Park City Mathematics Series, vol. 8, American Mathematical Society,
Providence, 2000, pp. 1-87.
Abstract.
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Intertwining operators and small unitary representations,
The Mathematical Legacy of Harish-Chandra; An AMS Special Session Honoring
the Memory of Harish-Chandra, Baltimore, 1998, Proceedings of Symposia in
Pure Mathematics 68 (2000), American Mathematical Society, Providence, Rhode
Island, pp. 403-431.
Abstract.
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Nomination for David A. Vogan Jr. as President Elect of the American
Mathematical Society,
Notices of the American Mathematical Society 48 (2001), 853-854.
Abstract |
Reprint in PDF.
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Representation Theory of Semisimple Groups: An Overview Based on
Examples, paperback reprint of the original 1986 hardback edition, Princeton
Landmarks in Mathematics, Princeton University Press, 2001.
ISBN: 0-691-09089-0.
Access to the table of contents,
the two prefaces, and a list of corrections.
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Branching theorems for compact symmetric spaces, Representation Theory
5 (2001), 404-436.
Abstract |
Reprint in PDF.
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Lie Groups Beyond an Introduction, Second Edition,
Progress in Mathematics, Vol. 140,
Birkhäuser, Boston, 2002. ISBN: 0-8176-4259-5.
Access to files of corrections,
the table of contents, the two prefaces, and abstracts
of chapters new or substantially changed from the first edition.
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The Gindikin-Karpelevic formula and intertwining operators, Lie
Groups and Symmetric Spaces, In Memory of F. I. Karpelevich, American
Mathematical Society Translations (2), 210 (2003), 145-159.
Abstract
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Geometric interpretations of two branching theorems of D.E. Littlewood,
Journal of Algebra 270 (2003), 728-754.
Abstract | Reprint in PDF.
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Analytic continuation of nonholomorphic discrete series for classical groups,
Noncommutative Harmonic Analysis in Honor of Jacques Carmona,
Progress in Mathematics, Vol. 220,
Birkhäuser, Boston, 2004, pp. 253-289.
ISBN: 0-8176-3207-7.
Abstract |
Reprint in PDF.
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Nilpotent orbits and some small unitary representations of indefinite
orthogonal groups, Journal of Functional Analysis 209 (2004), 36-100.
Abstract | Reprint in PDF.
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Salomon Bochner, August 20, 1899--May 2, 1982, Biographical Memoirs
85 (2004), 40-61.
Abstract |
Reprint in PDF.
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``Armand Borel (1923-2003),'' editor's note to article with eight authors,
Notices of the American Mathematical Society 51 (2004), 500; republished in
Asian Journal of Mathematics 8, No. 4 (2004), pp. xlvii-xlix.
Reprint of Noticespage in
PDF.
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``Weil's letter to his sister,'' letter to the editor, Notices of the
American Mathematical Society 52 (2005), 598-599.
Reprint in PDF.
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Basic Real Analysis, Cornerstones, Birkhäuser, Boston, 2005.
ISBN: 0-8176-3250-6.
Access to files of front matter,
sample pages from three chapters, and a list of corrections.
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Advanced Real Analysis, Cornerstones, Birkhäuser, Boston, 2005.
ISBN: 0-8176-4382-6.
Access to files of front matter,
sample pages from four chapters, and a short list of corrections.
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Basic Algebra, Cornerstones, Birkhäuser, Boston, 2006.
ISBN: 0-8176-3248-4.
Access to files of front matter,
sample pages from five chapters, and a short list of corrections.
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(with Henri Carayol) Limits of discrete series with infinitesimal
character zero, Transactions of the American Mathematical Society 359
(2007), 5611-5651.
Abstract | Reprint in PDF.
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Advanced Algebra, Cornerstones, Birkhäuser, Boston, 2007.
ISBN: 0-8176-4522-5.
Access to files of front matter and to
sample pages from five chapters.
Book reviews
-
Review of Lie Groups, Lie Algebras, and Their Representations by
V. S. Varadarajan and Compact Lie Groups and Their Representations by
D. P. Zhelobenko, Bulletin of the American Mathematical Society 81
(1975), 865-872.
- Review of Unitary Representations of Reductive Lie Groups by D.
A. Vogan, Bulletin of the American Mathematical Society (N.S.) 21
(1989), 380-384.
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Review of Matrix Groups: An Introduction to Lie Group Theory by
Andrew Baker and Lie Groups: An Introduction Through Linear Groups by
Wulf Rossmann, American Mathematical Monthly 110 (2003), 446-455.
Abstract |
Reprint in PDF.
Other items
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Certification of algorithm 42, Communications of the Association for
Computing Machinery 4(11) (1961), 498.
- (with S. J. Garland) Evaluation of Jacobi symbol, Communications of
the Association for Computing Machinery 5(6) (1962), 345-346.
Last modified: 11/5/07