Combinatorial Theory

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 related Heisenberg operators on a Fock space, we prove Cauchy and Pieri identities for super LLT polynomials, simultaneously generalizing the Cauchy, dual Cauchy, and Pieri 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 Pieri and Cauchy identities.

Mathematics Subject Classifications: 05E05, 82B20, 05E10

Keywords: Lattice models, super LLT polynomials