Free fermion six vertex model: symmetric functions and random domino tilings

Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying free fermion condition. Two families of $$F_\lambda ,G_\lambda $$ are defined as certain partition model, variables corresponding to row rapidities, labeling signatures $$\lambda =(\lambda _1\ge \ldots \ge \lambda _N)\in {\mathbb {Z}}^N$$ encoding boundary conditions. These generalize Schur polynomials, well some their variations, such factorial supersymmetric polynomials. Cauchy type summation identities for skew counterparts follow from Yang–Baxter equation. Using algebraic Bethe Ansatz, we obtain a double alternant formula Sergeev–Pragacz $$G_\lambda . In spirit theory processes, define probability measures sequences weights proportional products our functions. We show that these can be viewed determinantal point express correlation kernels in contour integral form. present two proofs: The first is direct computation Eynard–Mehta type, second uses non-standard, versions fermionic operators Fock space coming Ansatz model. also interpret processes random domino tilings half-strip weights. bulk, lattice asymptotic behavior described by new process $${\mathbb {Z}}^{2}$$ , which an doubly-inhomogeneous generalization extended discrete sine process.