Generation of Matrix Models by W-operators

TL;DR

This paper demonstrates how partition functions of diverse matrix models can be generated using W-operators, providing new matrix-model representations and illustrating their application to several well-known models.

Contribution

It introduces a method to derive matrix model partition functions via W-operators from elementary functions, expanding the understanding of their algebraic structure.

Findings

Partition functions obtained by W-operators for various models

Representation of models within the W_3-algebra framework

Elegant matrix-model representations for specific cases

Abstract

We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in external field and the Hurwitz-Kontsevitch model, for which we suggest an elegant matrix-model representation. In all these examples, the relevant W-operators belong to the W_3-algebra.