Abstract
We introduce a new family of Schur functions sλ/μ;a,b(x/y) that depend on two sets of variables and two sequences of parameters. These free fermionic Schur functions generalize and unify double, supersymmetric, and dual Schur functions from literature. These functions have a hidden symmetry that is manifested in the supersymmetric Cauchy identity∑λsλ;a,b(x/y)sˆλ;a,b(z/w)=∏i,j1+yizj1−xizj1+xiwj1−yiwj, where sˆλ;a,b(z/w)=sλ′;b′,a′(w/z) are the dual functions.Our approach is based on the integrable six vertex model with free fermionic Boltzmann weights. We show that these weights satisfy the refined Yang-Baxter equations, which allows us to prove the generalizations of well-known properties of the Schur functions. We emphasize that some of our results and proofs are novel even in special cases.
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