2013/05/03 by Rosengren, Hjalmar
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1305.0666
We study certain symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with Δ=± 1/2. 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 Γ0(12). In subsequent papers, we will show that the polynomials satisfy a non-stationary Schrödinger equation related to the Knizhnik--Zamolodchikov--Bernard equation and that they give a four-dimensional lattice of tau functions of Painlevé VI.