Elliptic orthogonal polynomials and their integrability.

Harini Desiraju
Sydney Mathematical Research Institute, University of Sydney

Elliptic orthogonal polynomials are a family of special functions that satisfy certain orthogonality condition with respect to a weight function on an elliptic curve. I will present a generalized framework using Riemann-Hilbert analysis to study such polynomials and obtain associated discrete and continuous integrable systems. As a quick check, for the simplest weight function, I will show that the elliptic formulation of the sixth Painlevé equation can be recovered.

Back to Workshop IV: Vertex Models: Algebraic and Probabilistic Aspects of Universality