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Quantum Fields and Strings Group Seminar
Quantum Fields and Strings Group Seminar
Operator description of (q,t)-matrix models as Macdonald hypergeometric functions
Operator description of (q,t)-matrix models as Macdonald hypergeometric functions
Organizers
Speaker
Victor Mishnyakov
Time
Thursday, April 2, 2026 2:30 PM - 4:00 PM
Venue
A7-302
Online
Zoom 388 528 9728
(BIMSA)
Abstract
Integrals of q-discrete-type measures of Macdonald polynomials have a very special form, with examples such as the Cherednik–Macdonald–Mehta identities and q-Kadell integrals. This family of integrals appears as partition functions of 3d supersymmetric gauge theories or as conformal blocks of q-deformed CFTs. We study an algebraic description of this property in terms of operator equations in the quantum toroidal gl1 algebra. These arise as a result of solving (q,t)-Virasoro constraints.The resulting partition functions are examples of Macdonald-type A_n hypergeometric functions and are related to multivariable orthogonal polynomials.