On the Deligne–Lusztig involution for character sheaves
- Autores: Alexander Yom Din
- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 3, 2019
- Idioma: inglés
- DOI: 10.1007/s00029-019-0495-6
- Enlaces
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Resumen
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).
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