Abstract:
In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves to a larger class of simple perverse sheaves which behaves well with respect to tensor product (unlike the character sheaves themselves).
Key words and phrases:character sheaf, perverse sheaf, tensor product.
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