AGT relations for sheaves on surfaces

Neguţ, Andrei¹

¹ Department of Mathematics, MIT, Cambridge, MA, United States, Simion Stoilow Institute of Mathematics, Bucharest, Romania

Geometry & topology, Tome 27 (2023) no. 8, pp. 3061-3094.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.3061

Keywords: moduli spaces of sheaves on surfaces, Ext operator, AGT correspondence

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