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Truncated convolution of character sheaves
by George Lusztig

Vol. 10 No. 1 (2015) P.1~P.72

ABSTRACT

Let $\textit{G}$ be a reductive, connected algebraic group over an algebraic closure of a finite field. We define a tensor structure on the category of perverse sheaves on $\textit{G}$ which are direct sums of unipotent character sheaves in a fixed two-sided cell; we show that this is equivalent to the centre with a known monoidal abelian category (a categorification of the $\textit{J}$-ring associated to the same two-sided cell).

KEYWORDS
Character sheaf, perverse sheaf, convolution, Weyl group.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20G99

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