On the Casselman-Jacquet functor

T. H. Chen, D. Gaitsgory, A. Yom Din

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

We study the Casselman-Jacquet functor J, viewed as a functor from the (derived) category of (g, K)-modules to the (derived) category of (g, N )-modules, N is the negative maximal unipotent. We give a functorial definition of J as a certain right adjoint functor, and identify it as a composition of two averaging functors AvN − ! ◦ AvN∗ . We show that it is also isomorphic to the composition AvN ∗ ◦ AvN! . Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) D-modules on an algebraic stack.

Original languageAmerican English
Title of host publicationRepresentations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017
EditorsAvraham Aizenbud, Dmitry Gourevitch, Erez M. Lapid, David Kazhdan
PublisherAmerican Mathematical Society
Pages73-112
Number of pages40
ISBN (Print)9781470442842
DOIs
StatePublished - 2019
Externally publishedYes
EventConference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017 - Jerusalem, Israel
Duration: 11 Jun 201716 Jun 2017

Publication series

NameProceedings of Symposia in Pure Mathematics
Volume101
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X

Conference

ConferenceConference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017
Country/TerritoryIsrael
CityJerusalem
Period11/06/1716/06/17

Bibliographical note

Publisher Copyright:
© 2019 American Mathematical Society.

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