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

Year: 2024

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae223

Author: Ilya Dumanski

Institutions: National Research University Higher School of Economics, Massachusetts Institute of Technology

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4403501442

FWCI: 0.671

Cites: 50

Cited by: 1

Related to: 10