Bow diagrams, Hanany-Witten moves and R-matrices of quantum toroidal algebra

Yegor Zenkevich (University of Edinburgh)

Tuesday 19th November 16:00-17:00 Maths 311B

Abstract

Bow varieties are generalizations of Nakajima quiver varieties that are inspired by brane constructions of supersymmetric gauge theories in three dimensions. We develop an algebraic formalism describing K-theoretic vertex functions counting quasimaps from P^1 into bow varieties. In the formalism the vertex functions are constructed as matrix elements of intertwining operators between representations of the quantum toroidal algebra of type gl_1. This correspondence allows us to prove that the vertex functions are eigenfunctions of certain difference operators, and also produces some interesting new identities for the R-matrix of the quantum toroidal algebra.

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