Superintegrability for some (q,t)-deformed matrix models

2025/10/21 by Liu, Fan, Wang, Rui, Yang, Jie +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.18524

Abstract

We analyze the Macdonald's (q,t)-deformed hypergeometric functions with one and two set variables and present their constraints. We prove the uniqueness to the solution of these constraints. We propose a concise method to prove the superintegrability relations for some well-known (q,t)-deformed matrix models, where the constraints of hypergeometric functions play a crucial role.

Citations

• Superintegrability of q,t-matrix models and quantum toroidal algebra recursions
• Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains
• Matrix models for the nested hypergeometric tau-functions
• q-Virasoro constraints in matrix models
• Hypergeometric Functions II (q-analogues)
• Cherednik algebras, W algebras and the equivariant cohomology of the\n moduli space of instantons on A²
• Refined Chern-Simons Theory and Knot Homology
• Tau Functions and Matrix Integrals
• Elliptic Selberg integrals
• Multivariable Al-Salam & Carlitz polynomials associated with the type A q-Dunkl kernel
• Generalization and Deformation of Drinfeld quantum affine algebras

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• Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials