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 language | English |
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Title of host publication | Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017 |
Editors | Avraham Aizenbud, Dmitry Gourevitch, Erez M. Lapid, David Kazhdan |
Publisher | American Mathematical Society |
Pages | 73-112 |
Number of pages | 40 |
ISBN (Print) | 9781470442842 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Event | Conference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017 - Jerusalem, Israel Duration: 11 Jun 2017 → 16 Jun 2017 |
Publication series
Name | Proceedings of Symposia in Pure Mathematics |
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Volume | 101 |
ISSN (Print) | 0082-0717 |
ISSN (Electronic) | 2324-707X |
Conference
Conference | Conference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017 |
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Country/Territory | Israel |
City | Jerusalem |
Period | 11/06/17 → 16/06/17 |
Bibliographical note
Publisher Copyright:© 2019 American Mathematical Society.