TY - JOUR
T1 - On the Deligne–Lusztig involution for character sheaves
AU - Yom Din, Alexander
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=85069746175&partnerID=8YFLogxK
U2 - 10.1007/s00029-019-0495-6
DO - 10.1007/s00029-019-0495-6
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AN - SCOPUS:85069746175
SN - 1022-1824
VL - 25
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 3
M1 - 49
ER -