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AGT relations for sheaves on surfaces

Andrei Neguţ

Geometry & Topology 27 (2023) 3061–3094
Abstract

We consider a natural generalization of the Carlsson–Okounkov Ext operator on the K–theory groups of the moduli spaces of stable sheaves on a smooth projective surface. We compute the commutation relations between the Ext operator and the action of the deformed W–algebra on K–theory, which was developed by the author in previous work. The conclusion is that the Ext operator is closely related to a vertex operator, thus giving a mathematical incarnation of the Alday–Gaiotto–Tachikawa correspondence for a general algebraic surface.

Keywords
moduli spaces of sheaves on surfaces, Ext operator, AGT correspondence
Mathematical Subject Classification
Primary: 14J60
Secondary: 14D21
References
Publication
Received: 26 May 2020
Revised: 9 March 2022
Accepted: 19 March 2022
Published: 9 November 2023
Proposed: Richard P Thomas
Seconded: Lothar Göttsche, Mark Gross
Authors
Andrei Neguţ
Department of Mathematics
MIT
Cambridge, MA
United States
Simion Stoilow Institute of Mathematics
Bucharest
Romania

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