Raising and Lowering Operators for Askey-Wilson Polynomials

Details Raising and Lowering Operators for Askey-Wilson Polynomials Raising and Lowering Operators for Askey-Wilson Polynomials

2007-01-04

arxiv.org/abs/math/0701134v1

SIGMA 3 (2007), 002, 11 pages

Mathematics

Quantum Algebra

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.002

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.

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