A Vertex Model for Supersymmetric LLT Polynomials

TL;DR

This paper introduces a new integrable vertex model that provides a combinatorial framework for supersymmetric LLT polynomials, enabling proofs of key identities and properties of these functions.

Contribution

It presents a novel vertex model realization for supersymmetric LLT polynomials, facilitating new proofs and generalizations of their identities.

Findings

Established a Yang-Baxter integrable vertex model for supersymmetric LLT polynomials.

Derived a Cauchy identity for these polynomials using the vertex model formalism.

Generalized known identities for supersymmetric Schur polynomials within this framework.

Abstract

We describe a Yang-Baxter integrable vertex model, which can be realized as a degeneration of a vertex model introduced by Aggarwal, Borodin, and Wheeler. From this vertex model, we construct a certain class of partition functions that we show are essentially equal to the super ribbon functions of Lam. Using the vertex model formalism, we give proofs of many properties of these polynomials, namely a Cauchy identity and generalizations of known identities for supersymmetric Schur polynomials.