RelRepDist SIGNED
Relative representation theory and distributions on reductive groups over local fields
Total Cost €
0EC-Contrib. €
0Partnership
0Views
0RelRepDist project word cloud
Explore the words cloud of the RelRepDist project. It provides you a very rough idea of what is the project "RelRepDist" about.
Project "RelRepDist" data sheet
The following table provides information about the project.
| Coordinator |
WEIZMANN INSTITUTE OF SCIENCE
Organization address contact info |
| 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.
| # | ||||
|---|---|---|---|---|
| 1 | WEIZMANN INSTITUTE OF SCIENCE | IL (REHOVOT) | coordinator | 1˙196˙215.00 |
Map
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 |
|---|---|---|---|
| 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 |
Are you the coordinator (or a participant) of this project? Plaese send me more information about the "RELREPDIST" project.
For instance: the website url (it has not provided by EU-opendata yet), the logo, a more detailed description of the project (in plain text as a rtf file or a word file), some pictures (as picture files, not embedded into any word file), twitter account, linkedin page, etc.
Send me an email (fabio@fabiodisconzi.com) and I put them in your project's page as son as possible.
Thanks. And then put a link of this page into your project's website.
The information about "RELREPDIST" are provided by the European Opendata Portal: CORDIS opendata.