Higher rank elliptic partition functions and multisymmetric elliptic functions

TL;DR

This paper introduces higher rank elliptic partition functions extending previous models, characterizes them through nested analysis, and provides explicit forms for rational, trigonometric, and elliptic cases, advancing the understanding of multisymmetric elliptic functions.

Contribution

It develops a new class of $rak{gl}_{M+1}$ partition functions with explicit forms, extending prior work and employing nested Izergin-Korepin analysis.

Findings

Explicit forms for rational, trigonometric, and elliptic partition functions.

Extension of multisymmetric functions to higher rank cases.

Characterization of partition functions via nested analysis.

Abstract

We introduce and investigate a class of $\mathfrak{gl}_{M+1}$ partition functions which is an extension of the one introduced by Foda-Manabe. We characterize the partition functions by a nested version of Izergin-Korepin analysis, and determine the explicit forms, for each of the rational, trigonometric and elliptic versions. The resulting multisymmetric functions can be regarded as extensions of the rational, trigonometric and elliptic weight functions.