On tensor categories attached to cells in affine Weyl groups. III. (English) Zbl 1210.20004

Bezrukavnikov, Roman; Finkelberg, Michael; Ostrik, Victor

Isr. J. Math. 170, 207-234 (2009).

Summary: We prove a weak version of Lusztig’s conjecture on explicit description of the asymptotic Hecke algebras (both finite and affine) related to monodromic sheaves on the base affine space (both finite and affine), and explain its relation to Lusztig’s classification of character sheaves.
For part II cf. R. Bezrukavnikov and V. Ostrik, Adv. Stud. Pure Math. 40, 101-119 (2004; Zbl 1078.20045).

MSC:

20C08	Hecke algebras and their representations
20G05	Representation theory for linear algebraic groups
20F55	Reflection and Coxeter groups (group-theoretic aspects)

Keywords:

tensor categories; two-sided cells; affine Weyl groups; asymptotic affine Hecke algebras; Lusztig conjecture

Citations:

Zbl 1078.20045

References:

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