Derived categories of character sheaves

Abstract

We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a corollary, we identify the category of character sheaves on $G$ as the category of quasi-coherent sheaves on an explicitly defined derived stack $\hat{G}$.

This ver: Add some prelimary on dg categories; calculate endomorphism complexes of irreducible character sheaves; fix some errors. ver.2: Fix some errors. Add examples for rank up to three. 9 pages, 7 figures