Elliptic $q,t$ matrix models

TL;DR

This paper introduces an elliptic deformation of the Gaussian $q,t$ matrix model, exploring the properties of symmetric functions that preserve key matrix model characteristics in this new setting.

Contribution

It extends the Gaussian $q,t$ matrix model to an elliptic case by deforming the density and Vandermonde factor, analyzing associated symmetric functions.

Findings

Established the elliptic $q,t$ matrix model framework

Identified symmetric functions maintaining matrix model properties

Provided insights into the structure of the elliptic deformation

Abstract

The Gaussian matrix model is known to deform to the $q,t$-matrix model. We consider further deformation to the elliptic $q,t$ matrix model by properly deforming the Gaussian density as well as the Vandermonde factor. Properties of an associated basis of symmetric functions that provide the matrix model property $<char>\sim {\rm char}$ in the deformed elliptic case are discussed.