A Geometric Approach to Feigin–Loktev Fusion Product and Cluster Relations in Coherent Satake Category

Abstract We propose a geometric realization of the Feigin–Loktev fusion product of graded cyclic modules over the current algebra. This allows us to compute it in several new cases. We also relate the Feigin–Loktev fusion product to the convolution of perverse coherent sheaves on the affine Grassman...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2024-11, Vol.2024 (22), p.13988-14007
Main Author: Dumanski, Ilya
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Abstract We propose a geometric realization of the Feigin–Loktev fusion product of graded cyclic modules over the current algebra. This allows us to compute it in several new cases. We also relate the Feigin–Loktev fusion product to the convolution of perverse coherent sheaves on the affine Grassmannian of the adjoint group. This relation allows us to establish the existence of exact triples, conjecturally corresponding to cluster relations in the Grothendieck ring of coherent Satake category.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnae223