Toward AGT for Parabolic Sheaves
Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.
2012 ◽
Vol 319
(1)
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pp. 269-301
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2010 ◽
Vol 25
(31)
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pp. 5595-5645
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2020 ◽
Vol 35
(06)
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pp. 2050021
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