On the Casselman-Jacquet functor

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

doi:10.1090/pspum/101/01791

On the Casselman-Jacquet functor

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 Av^{N −} ! ◦ Av^N∗ . We show that it is also isomorphic to the composition Av^N⁻ ∗ ◦ Av^N! . 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
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	https://doi.org/10.1090/pspum/101/01791
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
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
Country/Territory	Israel
City	Jerusalem
Period	11/06/17 → 16/06/17

Bibliographical note

Publisher Copyright:
© 2019 American Mathematical Society.

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10.1090/pspum/101/01791

Cite this

Chen, T. H., Gaitsgory, D., & Din, A. Y. (2019). On the Casselman-Jacquet functor. In A. Aizenbud, D. Gourevitch, E. M. Lapid, & D. Kazhdan (Eds.), Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017 (pp. 73-112). (Proceedings of Symposia in Pure Mathematics; Vol. 101). American Mathematical Society. https://doi.org/10.1090/pspum/101/01791

Chen, T. H. ; Gaitsgory, D. ; Din, A. Yom. / On the Casselman-Jacquet functor. Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017. editor / Avraham Aizenbud ; Dmitry Gourevitch ; Erez M. Lapid ; David Kazhdan. American Mathematical Society, 2019. pp. 73-112 (Proceedings of Symposia in Pure Mathematics).

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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.",

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doi = "10.1090/pspum/101/01791",

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Chen, TH, Gaitsgory, D & Din, AY 2019, On the Casselman-Jacquet functor. in A Aizenbud, D Gourevitch, EM Lapid & D Kazhdan (eds), Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017. Proceedings of Symposia in Pure Mathematics, vol. 101, American Mathematical Society, pp. 73-112, Conference on Representation Theory and Algebraic Geometry held in honor of Joseph Bernstein, 2017, Jerusalem, Israel, 11/06/17. https://doi.org/10.1090/pspum/101/01791

On the Casselman-Jacquet functor. / Chen, T. H.; Gaitsgory, D.; Din, A. Yom.
Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017. ed. / Avraham Aizenbud; Dmitry Gourevitch; Erez M. Lapid; David Kazhdan. American Mathematical Society, 2019. p. 73-112 (Proceedings of Symposia in Pure Mathematics; Vol. 101).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Chen TH, Gaitsgory D, Din AY. On the Casselman-Jacquet functor. In Aizenbud A, Gourevitch D, Lapid EM, Kazhdan D, editors, Representations of Reductive Groups - Conference in honor of Joseph Bernstein Representation Theory and Algebraic Geometry, 2017. American Mathematical Society. 2019. p. 73-112. (Proceedings of Symposia in Pure Mathematics). doi: 10.1090/pspum/101/01791

On the Casselman-Jacquet functor

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