Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Representation Theory

arXiv:1507.00606 (math)
[Submitted on 2 Jul 2015 (v1), last revised 24 May 2017 (this version, v3)]

Title:A Formula for the Geometric Jacquet Functor and its Character Sheaf Analogue

Authors:Tsao-Hsien Chen, Alexander Yom Din
View PDF
Abstract:Let (G,K) be a symmetric pair over the complex numbers, and let X=K\G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to MN\G, which we call the "wonderful degeneration". We show that on the category of character sheaves on X, this functor is isomorphic to a composition of two averaging functors (a parallel result, on the level of functions in the p-adic setting, was obtained in [BK, SV]). As an application, we obtain a formula for the geometric Jacquet functor of [ENV] and use this formula to give a geometric proof of the celebrated Casselman's submodule theorem and establish a second adjointness theorem for Harish-Chandra modules.
Comments: Revised version. Equivariancy replaces stratification arguments, so that the results are applicable to all sheaf settings
Subjects: Representation Theory (math.RT)
Cite as: arXiv:1507.00606 [math.RT]
  (or arXiv:1507.00606v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1507.00606

Submission history

From: Alexander Yom Din [view email]
[v1] Thu, 2 Jul 2015 14:41:34 UTC (38 KB)
[v2] Tue, 27 Sep 2016 22:14:11 UTC (40 KB)
[v3] Wed, 24 May 2017 17:13:59 UTC (39 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.RT
< prev   |   next >
new | recent | 2015-07
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)