1305.0666 (Hjalmar Rosengren)

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

Hjalmar Rosengren

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 Schr\"odinger equation related to the Inozemtsev model and that they give a four-dimensional lattice of tau functions of Painlev\'e VI.

View original: http://arxiv.org/abs/1305.0666