  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.
