Notes on character sheaves

TL;DR

This paper studies a functor related to character sheaves, computes it in a Grothendieck group considering weights, and extends the class of character sheaves to include simple perverse sheaves with better tensor product properties.

Contribution

It introduces an extension of character sheaves to a broader class of simple perverse sheaves with improved tensor product behavior.

Findings

Computed the functor in the Grothendieck group considering weights.

Extended character sheaves to a larger class with better tensor properties.

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 under tensor product (unlike the character sheaves themselves).