Two proofs of a Jantzen conjecture for Whittaker modules

Thumbnail Image

Files

two_proofs_of_a_jantzen_conje-20260721155049781938.pdf (906.65 KB)

Date issued

2025

Authors


Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Reuse License

CC-BY-4.0
Description of rights: CC-BY-4.0
Item type:Item, ZeitschriftenaufsatzAccess status: Open Access ,

Abstract

We define a filtration of a standard Whittaker module over a complex semisimple Lie algebra and and establish its fundamental properties. Our filtration specializes to the Jantzen filtration of a Verma module for a certain choice of parameter. We prove that embeddings of standard Whittaker modules are strict with respect to our filtration, and that the filtration layers are semisimple. This provides a generalization of the Jantzen conjectures to Whittaker modules. We prove these statements in two ways. First, we give an algebraic proof which compares Whittaker modules to Verma modules using a functor introduced by Backelin. Second, we give a geometric proof using mixed twistor D-modules.

DOI

https://doi.org/10.25358/openscience-15470

Description

Keywords

Citation

URI

https://openscience.ub.uni-mainz.de/handle/20.500.12030/15491

Published in

Selecta mathematica, 31, Birkhäuser, Basel [u.a.] ; Berlin, 2025, https://doi.org/10.1007/s00029-025-01057-2

Collections

DFG-491381577-H

Endorsement

Review

Supplemented By

Referenced By