Exotic t-structures and actions of quantum affine algebras

TL;DR

This paper introduces a method to construct exotic t-structures using quantum affine algebra actions, leveraging different algebraic realizations, with applications in geometric Langlands, knot theory, and representation theory.

Contribution

It provides a systematic approach to building exotic t-structures via quantum affine algebra actions and connects various geometric and algebraic frameworks.

Findings

Constructed exotic t-structures on convolution varieties.

Linked quantum affine algebra realizations to geometric Langlands.

Reproduced known exotic t-structures in type A.

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--Mirkovic on the (Grothendieck--)Springer resolution in type A.