Representations of Reductive Groups

466 Pages·2019·4.631 MB·English

by  Dmitry Gourevitch (editor), David Kazhdan (editor), Erez M. Lapid (editor)

Proceedings of Symposia in
P M
URE ATHEMATICS
Volume 101
Representations of
Reductive Groups
Conference in honor of Joseph Bernstein
Representation Theory & Algebraic Geometry
June 11–16, 2017
Weizmann Institute of Science, Rehovot, Israel
and The Hebrew University of Jerusalem, Is-
rael
Avraham Aizenbud
Dmitry Gourevitch
David Kazhdan
Erez M. Lapid
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
10.1090/pspum/101
Volume 101
Representations of
Reductive Groups
Conference in honor of Joseph Bernstein
Representation Theory & Algebraic Geometry
June 11–16, 2017
Weizmann Institute of Science, Rehovot, Israel
and The Hebrew University of Jerusalem, Is-
rael
Avraham Aizenbud
Dmitry Gourevitch
David Kazhdan
Erez M. Lapid
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
Proceedings of Symposia in
P M
URE ATHEMATICS
Volume 101
Representations of
Reductive Groups
Conference in honor of Joseph Bernstein
Representation Theory & Algebraic Geometry
June 11–16, 2017
Weizmann Institute of Science, Rehovot, Israel
and The Hebrew University of Jerusalem, Is-
rael
Avraham Aizenbud
Dmitry Gourevitch
David Kazhdan
Erez M. Lapid
Editors
Licensed to AMS.
License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms
2010 Mathematics Subject Classification. Primary 11F27, 11F70, 20C08, 20C33, 20G05,
20G20,20G25, 22E47.
Library of Congress Cataloging-in-Publication Data
Names: ConferenceonRepresentationTheoryandAlgebraicGeometryinhonorofJosephBern-
stein(2017: Jerusalem,Israel)|Aizenbud,Avraham,1983-editor. |Gourevitch,Dmitry,1981-
editor. | Kazhdan, D. A. (David A.), 1946- editor. | Lapid, Erez, 1971- editor. | Bernstein,
Joseph,1945-honoree.
Title: Representationsofreductivegroups: ConferenceonRepresentationTheoryandAlgebraic
Geometry in honor of Joseph Bernstein, June 11-16, 2017, The Weizmann Institute of Sci-
ence&TheHebrewUniversity ofJerusalem,Jerusalem,Israel/AvrahamAizenbud, Dmitry
Gourevitch,DavidKazhdan,ErezM.Lapid,editors.
Description: Providence, Rhode Island : American Mathematical Society, [2019] | Series: Pro-
ceedingsofsymposiainpuremathematics;Volume101|Includesbibliographicalreferences.
Identifiers: LCCN2018041948|ISBN9781470442842(alk. paper)
Subjects: LCSH:Representationsofgroups–Congresses. |Representationsofalgebras–Congresses.
Classification: LCCQA176.C6652019|DDC512/.22–dc23
LCrecordavailableathttps://lccn.loc.gov/2018041948
DOI:http://dx.doi.org/10.1090/pspum/101
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To Joseph Bernstein, in gratitude
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Contents
Preface ix
Character values and Hochschild homology
Roman Bezrukavnikov and David Kazhdan 1
Schwartz space of parabolic basic affine space and asymptotic Hecke algebras
Alexander Braverman and David Kazhdan 31
Explicit local Jacquet-Langlands correspondence: The non-dyadic wild case
Colin J. Bushnell and Guy Henniart 45
On the Casselman-Jacquet functor
T.-H. Chen, D. Gaitsgory, and A. Yom Din 73
Periods and theta correspondence
Wee Teck Gan 113
Generalized and degenerate Whittaker quotients and Fourier coefficients
Dmitry Gourevitch and Siddhartha Sahi 133
Geometric approach to the fermionic Fock space, via flag varieties and
representations of algebraic (super)groups
Caroline Gruson and Vera Serganova 155
Representations of a p-adic group in characteristic p
G. Henniart and M.-F. Vign´eras 171
On the support of matrix coefficients of supercuspidal representations of the
general linear group over a local non-archimedean field
Erez Lapid 211
On the generalized Springer correspondence
G. Lusztig 219
The modular pro-p Iwahori-Hecke Ext-algebra
Rachel Ollivier and Peter Schneider 255
Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda on the
Plancherel density
Eric Opdam 309
Limiting cycles and periods of Maass forms
Andre Reznikov 351
vii
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viii CONTENTS
On vector-valued twisted conjugation invariant functions on a group; with an
appendix by Stephen Donkin
Liang Xiao and Xinwen Zhu 361
Local theta correspondence and nilpotent invariants
Chen-Bo Zhu 427
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Preface
The conference “Representation Theory and Algebraic Geometry” took place
onJune11-16,2017attheWeizmannInstituteofScienceandtheHebrewUniversity
of Jerusalem. The conference honored Joseph Bernstein upon his 72nd birthday
and his recent retirement from Tel Aviv University.
Representation theory in its broadest sense is one of the areas that Joseph
Bernstein has fundamentally transformed through his seminal contributions, to-
gether with many of his collaborators. An in-depth account of the Mathematics
of Joseph Bernstein appeared recently in the special 2016 issue of Selecta Mathe-
matica, which also contains some of the topics not covered by these proceedings.
Suffice it to say that Bernstein has had a towering influence on Mathematics, in
particularinIsrael,throughhiswritings,guidanceofstudents,communicationwith
colleagues and generously sharing his ideas.
The papers in this volume are mostly authoredby the conferencespeakers and
their collaborators, although the contents do not necessarily match exactly with
the lectures themselves. While the underlying theme is representation theory, the
papers are quite diverse. The lion’s share of the papers concerns different aspects
of representations of p-adic groups and Hecke algebras, including in characteristic
p. Even here, the papers differ significantly in methodology and emphasis and rep-
resent the full spectrum of techniques from the algebraic to the analytic. Other
topics, such as representations of finite groups, real groups and supergroups, an-
alytic aspects of automorphic forms and invariant theory are also covered. This
diversity reflects the wide interests of Joseph Bernstein in representation theory
and beyond.
We would like to thank all the speakers of the conference, most of whom con-
tributed to this volume. We are also very grateful to the many referees for this
volume whose assiduous and selfless work was absolutely crucial.
Theconferencewasthepinnacleofaspecialtrimesteronrepresentationtheory
of reductive groups over local fields and applications to automorphic forms, which
took place at the Weizmann Institute in the spring of 2017. Altogether there
were over 150 participants including more than 100 foreign visitors. We take this
opportunitytothankthemall, bothlecturersandstudents whomadethisevent so
successful.
The conference and the trimester were made possible by the generous support
of the Chorafas Institute for Scientific Exchange, the Arthur and Rochelle Belfer
Institute, the Israel Science Foundation and the European Research Council. We
thank these organizations wholeheartedly.
Lastbutnotleast,wethanktheadministrativestaffoftheWeizmannInstitute,
especially at the faculty of Mathematics and Computer Science, as well as that of
ix
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