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SIGMA 3 (2007), 002, 11 pages math.QA/0701134
https://doi.org/10.3842/SIGMA.2007.002
Contribution to the Vadim Kuznetsov Memorial Issue
Raising and Lowering Operators for Askey-Wilson Polynomials
Siddhartha Sahi
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
Received September 20, 2006, in final form December 27, 2006; Published online January 04, 2007
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.
Key words:
orthogonal polynomials; Askey-Wilson polynomials; q-difference equation; three term recurrence; raising operators; lowering operators; root systems; double affine Hecke algebra.
pdf (223 kb)
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