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arXiv · 1308.1082

Truncated convolution of character sheaves

G. Lusztig
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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.

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G. Lusztig. 2014-02-17. Truncated convolution of character sheaves. https://arxiv.org/abs/1308.1082

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