Ilya Dumanski, MIT

Title: Coherent Satake category, Q-systems, and Feigin-Loktev fusion product

Abstract: Feigin--Loktev fusion product is an operation between graded cyclic modules over the current Lie algebra. We explain how it is related to monoidal operations in two other categories: modules over the quantum loop group and the category of perverse coherent sheaves on the affine Grassmannian. This relation may explain similarities between these two categories (most notably the cluster patterns). Moreover, this allows us to tranfer some results from one of these categories into another. Namely, we establish the existence of short exact sequences in the coherent Satake category, which are analogs of Q-systems, and which conjecturally stand for cluster mutations in this category. Based on arXiv:2308.05268.