Special polynomials related to the supersymmetric eight-vertex model. I. Behaviour at cusps

Preprint, 2013

We study certain symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models. In this paper, which is the first part of a series, we study the behaviour of the polynomials at special parameter values, which can be identified with cusps of the modular group Gamma_0(12). In subsequent papers, we will show that the polynomials satisfy a non-stationary Schrödinger equation related to the Inozemtsev model and that they give a four-dimensional lattice of tau functions of Painlevé VI.