MacMahon KZ equation for Ding-Iohara-Miki algebra
Panupong Cheewaphutthisakun, Hiroaki Kanno
TL;DR
This paper derives a generalized Knizhnik-Zamolodchikov equation for intertwiners of the Ding-Iohara-Miki algebra, linking it to refined topological vertices and supersymmetric gauge theories.
Contribution
It introduces a new generalized KZ equation for the algebra's intertwiners, connecting algebraic structures with topological vertex and gauge theory concepts.
Findings
Derived a generalized KZ equation for Ding-Iohara-Miki algebra intertwiners.
Identified solutions as ratios of two-point functions related to Nekrasov factors.
Linked algebraic intertwiners to refined topological vertices and supersymmetric theories.
Abstract
We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological vertex which is regarded as the intertwining operator of the Fock representation. The shift of the spectral parameter of the intertwiners is generated by the operator which is constructed from the universal matrix. The solutions to the generalized KZ equation are factorized into the ratio of two point functions which are identified with generalizations of the Nekrasov factor for supersymmetric quiver gauge theories
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