Exotic t-structures and actions of quantum affine algebras (Q2216736)

Summary: 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 \textit{R. Bezrukavnikov} and \textit{I. Mirković} [Ann. Math. (2) 178, No. 3, 835--919 (2013; Zbl 1293.17021)] on the (Grothendieck-)Springer resolution in type A.