Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations

Abstract

We construct the ($\beta$-deformed) partition function hierarchies with $W$-representations. Based on the $W$-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and Jack polynomials, respectively. Some well known superintegrable matrix models such as the Gaussian hermitian one-matrix model (in the external field), $N\times N$ complex matrix model, $\beta$-deformed Gaussian hermitian and rectangular complex matrix models are contained in the constructed hierarchies.

11 pages

References in corpus (8)

• Generation of Matrix Models by W-operators
• On KP-integrable Hurwitz functions
• Jack polynomials and free cumulants
• Virasoro constraints for Kontsevich-Hurwitz partition function
• Superintegrability of Kontsevich matrix model
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Complete solution to Gaussian tensor model and its integrable properties
• Natanzon-Orlov model and refined superintegrability

Cited by in corpus (1)

• Superintegrability as the hidden origin of Nekrasov calculus