On the Deligne–Lusztig involution for character sheaves

Alexander Yom Din*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For a reductive group G, we study the Drinfeld–Gaitsgory functor of the category of conjugation-equivariant D-modules on G. We show that this functor is an equivalence of categories, and that it has a filtration with layers expressed via parabolic induction of parabolic restriction. We use this to provide a conceptual definition of the Deligne–Lusztig involution on the set of isomorphism classes of irreducible character D-modules, which was defined previously in Lusztig (Adv Math 57:266–315, 1985, §15).

Original languageAmerican English
Article number49
JournalSelecta Mathematica, New Series
Volume25
Issue number3
DOIs
StatePublished - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

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