A Lattice Model for Supersymmetric LLT Polynomials
Location
LLT polynomials, originally known as ribbon functions, are a q-analogue of products of Schur polynomials. Sharing many of the same properties as Schur polynomials--they are symmetric, satisfy Cauchy identities, and can be written as a generating function over tableaux as well as in terms of operators on a Fock space representation--they were one of the inspirations for Lam's combinatorial generalization of the Boson-Fermion correspondence (arXiv:0507341).
I will discuss the supersymmetric analogue of LLT polynomials, known as superLLT polynomials, and present a solvable ribbon lattice model that produces them as its partition function. I will also prove the Cauchy identity for these polynomials using operators and compare it to a surprising solution to the Yang-Baxter equation that arises when we adapt the lattice model to stack atop itself in a Cauchy-identity-style model. This is joint work with Michael Curran, Calvin Yost-Wolff, Sylvester Zhang, and Valerie Zhang (arXiv:2110.07597).
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