Leonard pairs and Askey-Wilson relations
by Raimundas Vidunas
Abstract: A Leonard pair (A,B) is a pair of linear transformations on a
finite dimensional vector space, each having a tri-diagonal form with respect
to an eigenbasis of the other. They occur in representations of sl 2 and related algebras, or with some orthogonal polynomials and association schemes. If (A,B) is a Leonard pair, then A,B satisfy so called Askey-Wilson relations.
These are a pair of cubic non-commutative relations. One of the questions is, how many Leonard pairs can satisfy the same Askey-Wilson relations?
For More Information: Dr. Iwan Jensen Phone: +61 3 8344 5214 I.Jensen@ms.unimelb.edu.au