Twisted Whittaker category on affine flags and the category of representations of the mixed quantum group

Abstract

We prove the twisted Whittaker category on the affine flag variety and the category of representations of the mixed quantum group are equivalent. In particular, we prove that the quantum category O is equivalent to the category of twisted Whittaker D-modules on affine flags in the generic case.

69 pages, modified according to the referee report; v5, changed typos, references and acknowledgements