# Elliptic supersymmetric integrable model and multivariable elliptic functions

## TL;DR

This paper explores an elliptic integrable model extending the Perk-Schultz model, revealing that its partition functions can be expressed as products of elliptic factors and elliptic Schur-type functions, connecting integrable models with elliptic symmetric functions.

## Contribution

It introduces a new class of partition functions for the elliptic model and demonstrates their explicit expression as elliptic products and symmetric functions, advancing the understanding of elliptic integrable systems.

## Key findings

- Partition functions are expressed as products of elliptic factors and elliptic Schur-type functions.
- The results establish a connection between elliptic integrable models and elliptic symmetric functions.
- The work relates to recent number theory results on trigonometric models and Schur functions.

## Abstract

We investigate the elliptic integrable model introduced by Deguchi and Martin, which is an elliptic extension of the Perk-Schultz model. We introduce and study a class of partition functions of the elliptic model by using the Izergin-Korepin analysis. We show that the partition functions are expressed as a product of elliptic factors and elliptic Schur-type symmetric functions. This result resembles the recent works by number theorists in which the correspondence between the partition functions of trigonometric models and the product of the deformed Vandermonde determinant and Schur functions were established.