A vertex model for LLT polynomials

TL;DR

This paper introduces a new integrable vertex model that provides a novel combinatorial framework for LLT polynomials, enabling new proofs of their key properties and deepening understanding of their algebraic structure.

Contribution

It constructs a Yang-Baxter integrable vertex model that directly relates to LLT polynomials, offering new proof techniques and insights into their properties.

Findings

Vertex model exactly reproduces LLT polynomials

Provides alternative proofs of symmetry and Cauchy identity

Establishes integrability structure for LLT polynomials

Abstract

We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we give alternate proofs of many properties of these polynomials, including symmetry and a Cauchy identity.