Speaker
Michela Varagnolo
Description
I will present an equivalence between the category O for shifted quantum loop groups (associated with arbitrary Cartan matrices, including non-symmetric ones) and a module category over a new type of quiver Hecke algebra. This equivalence is based on the computation of the K-theoretic analogue of Coulomb branches with symmetrizers introduced by Nakajima and Weekes. At the decategorified level, this yields a connection between the Grothendieck group of O and a finite-dimensional module over a simple Lie algebra of unfolded symmetric type. In some cases, this module can be computed explicitly; more generally, one can describe its crystal structure via a combinatorial rule. Joint with Eric Vasserot.