Korina Digalaki: Structure Constants for Free-Fermion Six Vertex Model Symmetric Functions

Speaker
Korina Digalaki, Massachusetts Institute of Technology

Abstract
The free fermion six-vertex model symmetric functions $\mathsf{F}$ and $\mathsf{G}$, introduced by Aggarwal, Borodin, Petrov, and Wheeler, carry inhomogeneous row and column parameters and interpolate between ordinary, factorial, and supersymmetric Schur functions. I will present a product expansion $\mathsf{F}_\kappa\,\mathsf{G}_{\lambda/\mu} = \sum_\nu \mathcal{C}^{\nu}_{\kappa,\lambda/\mu}\,\mathsf{F}_\nu$, in which the structure constants are realized as partition functions of an integrable lattice region — a “puzzle.” The proof evaluates an auxiliary cubic configuration in two ways via the Yang–Baxter equation. In the Schur limit, these structure constants recover the classical Littlewood–Richardson coefficients. Joint work in preparation with Michael Wheeler.