A discrete system from the recurrence coefficients of 2-variable elliptic orthogonal polynomials
Seminar Room 1, Newton Institute
A new class of orthogonal polynomials are considered from a formal approach: a family of two-variable orthogonal polynomials related through an elliptic curve. The formal approach means we are interested in those relations that can be derived, without specifying a weight function.
Using generalized Sylvester identities, recurrence relations and bilinear relations between the recurrence coefficients are derived. These bilinear relations are shown to integrable in the sense that they have Lax pairs.