2021/10/14 by Michael Curran, Claire Frechette, Curran, Michael J. +7
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2110.07597
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.