Raising and Lowering Operators for Askey-Wilson Polynomials

Abstract

In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

Keywords

• orthogonal polynomials
• Askey-Wilson polynomials
• q-difference equation
• three term recurrence
• raising operators
• lowering operators
• root systems
• double affine Hecke algebra