# Leonard pairs and Askey-Wilson relations

#### by Raimundas Vidunas

Institution: Kyushu University, Japan
Date: Thu 7th September 2006
Time: 3:15 PM
Location: Hercus Theatre, Deptartment of Physics, The University of Melbourne

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