arXiv math/07011342007-01-04math.QAmath-phmath.MP

Raising and Lowering Operators for Askey-Wilson Polynomials

Siddhartha Sahi

备注：: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：: SIGMA 3 (2007), 002, 11 pages
DOI：: 10.3842/SIGMA.2007.002

英文摘要：

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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