Truncated convolution of character sheaves

2013/08/05 by G. Lusztig, Lusztig, G.
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1308.1082

openalex publication_date 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a reductive connected group over an algebraic closure of a finite field. I define a tensor structure on the category of perverse sheaves on G which are direct sums of unipotent character sheaves in a fixed two-sided cell, in accordance with a conjecture I have made in 2004. I also show that that the resulting monoidal category is equivalent to the centre of a monoidal category which I defined in 1997 (a categorical version of the J-ring attached to the same two-sided cell), thus verifying a conjecture of Bezrukavnikov, Finkelberg, Ostrik. A possible interpretation of unipotent characters associated to a finite noncrystallographic Coxeter group is given.

Citations

• The Character Theory of a Complex Group
• From subfactors to categories and topology II: The quantum double of tensor categories and subfactors

Related

• Non-unipotent character sheaves as a categorical centre
• Restriction of a character sheaf to conjugacy classes
• Character sheaves on disconnected groups, X
• Character sheaves on disconnected groups, I
• On the unipotent support of character sheaves