A Lattice Model for Super LLT Polynomials

TL;DR

This paper introduces a solvable lattice model for super LLT polynomials, proving a Cauchy identity and exploring connections to integrable systems, advancing the combinatorial and algebraic understanding of these symmetric functions.

Contribution

It presents a new lattice model for super LLT polynomials and establishes a generalized Cauchy identity using operator methods on Fock space.

Findings

Proved a Cauchy identity for super LLT polynomials.

Constructed a semi-infinite Cauchy lattice model with Yang-Baxter equation.

Connected the lattice model to algebraic identities of symmetric functions.

Abstract

We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for super LLT polynomials, simultaneously generalizing the Cauchy and dual Cauchy identities for LLT polynomials. Lastly, we construct a solvable semi-infinite Cauchy lattice model with a surprising Yang-Baxter equation and examine its connections to the Cauchy identity.