Exotic t-structures and actions of quantum affine algebras

Abstract

We explain how quantum affine algebra actions can be used to systematically construct "exotic" t-structures. The main idea, roughly speaking, is to take advantage of the two different descriptions of quantum affine algebras, the Drinfeld–Jimbo and the Kac–Moody realizations.

Our main application is to obtain exotic t-structures on certain convolution varieties defined using the Beilinson–Drinfeld and affine Grassmannians. These varieties play an important role in the geometric Langlands program, knot homology constructions, K-theoretic geometric Satake and the coherent Satake category. As a special case we also recover the exotic t-structures of Bezrukavnikov–Mirković [BM] on the (Grothendieck–)Springer resolution in type A.