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RelRepDist SIGNED

Relative representation theory and distributions on reductive groups over local fields

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EC-Contrib. €

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Project "RelRepDist" data sheet

The following table provides information about the project.

Coordinator
WEIZMANN INSTITUTE OF SCIENCE 

Organization address
address: HERZL STREET 234
city: REHOVOT
postcode: 7610001
website: www.weizmann.ac.il

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Project website http://www.wisdom.weizmann.ac.il/
 Total cost 1˙196˙215 €
 EC max contribution 1˙196˙215 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-03-01   to  2020-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    WEIZMANN INSTITUTE OF SCIENCE IL (REHOVOT) coordinator 1˙196˙215.00

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 Project objective

One can view the representation theory of a topological group as non-commutative harmonic analysis on the group. For compact groups this view is justified by the Peter-Weyl theorem. The relative representation theory of a group is harmonic analyses on spaces with transitive group action.

I work in relative representation theory of reductive (algebraic) groups over local fields, e.g. the general linear group over the field of real numbers or the field of p-adic numbers. This theory has applications to the theory of automorphic forms, in particular to the relative trace formula.

There are many similarities between the real and p-adic cases, and some results can be formulated uniformly for all local fields, but their proofs are usually specific to each type of local fields. An important tool in this theory, that is applicable for all local fields, is the analysis of equivariant distributions on the group. However, this analysis is quite different for the two kinds of fields.

In the first part of this proposal I describe my ongoing work on some tools that will help to approach invariant distributions uniformly for all fields. I also propose to advance, using those tools, towards the proofs of some long-standing conjectures on density of orbital integrals, comparison of Lie algebra homologies, and classification of (non-compact) Gelfand pairs.

The second part of this proposal concerns generalized Whittaker models, or equivalently harmonic analyses on the quotient of a reductive group by a unipotent subgroup. In 1987 Moeglen and Waldspurger comprehensively described the role of a representation in this harmonic analyses in terms of a certain collection of nilpotent orbits attached to this representation. This result, as well as previous results on Whittaker models have many applications in representation theory and in the theory of automorphic forms. I propose to obtain an archimedean analog of this result.

 Publications

year authors and title journal last update
List of publications.
2020 Gomez, Raul; Gourevitch, Dmitry; Sahi, Siddhartha
Whittaker supports for representations of reductive groups
published pages: , ISSN: 0373-0956, DOI:
To appear in Annales Institut Fourier 1 2019-11-07
2019 Gourevitch, Dmitry; Gustafsson, Henrik P. A.; Kleinschmidt, Axel; Persson, Daniel; Sahi, Siddhartha
A reduction principle for Fourier coefficients of automorphic forms
published pages: , ISSN: , DOI:
1 2019-11-07
2019 Rubio, Roberto
On the Gelfand property for complex symmetric pairs
published pages: , ISSN: , DOI:
arXiv 1 2019-11-07
2019 Dmitry Gourevitch, Eyal Kaplan
Multiplicity one theorem for the generalized doubling method
published pages: , ISSN: , DOI:
2019-10-28
2015 Shachar Carmeli
On the Stability and Gelfand Propertyof Symmetric Pairs
published pages: , ISSN: , DOI:
2019-06-05
2018 Dmitry Gourevitch, Siddhartha Sahi, Eitan Sayag
Analytic Continuation of Equivariant Distributions
published pages: , ISSN: 1073-7928, DOI: 10.1093/imrn/rnx326
International Mathematics Research Notices 2019-06-05
2017 Boaz Elazar, Ary Shaviv
Schwartz functions on real algebraic varieties
published pages: 1-25, ISSN: 0008-414X, DOI: 10.4153/CJM-2017-042-6
Canadian Journal of Mathematics 2019-06-05
2016 Avraham Aizenbud, Dmitry Gourevitch, Bernhard Krötz, Gang Liu
Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture
published pages: 979-992, ISSN: 0025-5874, DOI: 10.1007/s00209-016-1629-6
Mathematische Zeitschrift 283/3-4 2019-06-05
2018 Maxim Gurevich, Jia-Jun Ma, Arnab Mitra
On two questions concerning representations distinguished by the Galois involution
published pages: , ISSN: 0933-7741, DOI: 10.1515/forum-2016-0212
Forum Mathematicum 30/1 2019-06-05
2017 Itay Glazer
Representations of reductive groups distinguished by symmetric subgroups
published pages: , ISSN: 0025-5874, DOI: 10.1007/s00209-017-1961-5
Mathematische Zeitschrift 2019-06-05
2017 Raul Gomez, Dmitry Gourevitch, Siddhartha Sahi
Whittaker supports for representations of reductive groups
published pages: , ISSN: , DOI:
arXiv repository 2019-06-05

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