| Summary: | We prove the connection between the Nekrasov partition function of N= 2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations. Mathematically, this is achieved by relating the Carlsson-Okounkov Ext vector bundle on the moduli space of rank 2 sheaves with Liouville vertex operators. Our approach is geometric in nature, and uses a new method for intersection-theoretic computations of the Ext operator. Keywords: Nekrasov partition function, AGT relations, Ext operators, shuffle algebra
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