On tensor categories attached to cells in affine Weyl groups, III

By R. Bezrukavnikov, Michael Finkelberg, V. Ostrik. 2000

129 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cbaa8e79b65f9ee0786b812e6726d2799f7e81ae

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Categorification of (induced) cell modules and the rough structure of generalized Verma modules (2007, unknown): “This filtration is based on the Gelfand–Kirillov dimension which is closely related to Lusztig’s a-function (see [50]) and should be compared with the appearance of the a-function in [12] and [28].”
Kloosterman sheaves for reductive groups (2010, methodology): “[4] R. Bezrukavnikov, On tensor categories attached to cells in affine Weyl groups, in Representation Theory of Algebraic Groups and Quantum Groups, Adv.”
Module categories, weak Hopf algebras and modular invariants (2001, background): “[ 4 ]) Any indecomposable module category over Rep(G) is equivalent to Rep1(H, ω) for some H ⊂ G and ω ∈ H2(H, k∗).”
Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution (2013, background): “(An equivalent statement is that the set of ”centrally extended points” appearing in [BO] is actually a plain finite set with a Ge action.”