Raising and Lowering Operators for Askey-Wilson Polynomials
Copyright policy )Raising and Lowering Operators for Askey-Wilson Polynomials
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.
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/
- Rutgers, The State University of New Jersey United States
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson polynomials, Hecke algebra, q-difference equation, root systems, FOS: Physical sciences, lowering operators, Mathematical Physics (math-ph), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), raising operators, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, three term recurrence, Quantum Algebra (math.QA), double affine Hecke algebra, \(q\)-difference equation, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, orthogonal polynomials, Mathematics, Mathematical Physics
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson polynomials, Hecke algebra, q-difference equation, root systems, FOS: Physical sciences, lowering operators, Mathematical Physics (math-ph), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), raising operators, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, three term recurrence, Quantum Algebra (math.QA), double affine Hecke algebra, \(q\)-difference equation, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, orthogonal polynomials, Mathematics, Mathematical Physics
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