Dualities in the q -Askey Scheme and Degenerate DAHA
| Autor: | Marta Mazzocco, Tom H. Koornwinder |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Algebraic structure High Energy Physics::Lattice Applied Mathematics 010102 general mathematics Degenerate energy levels Mathematics::Classical Analysis and ODEs Duality (optimization) Eigenfunction 01 natural sciences Askey scheme Mathematics::Quantum Algebra 0103 physical sciences Orthogonal polynomials 010307 mathematical physics 0101 mathematics Eigenvalues and eigenvectors Mathematics Variable (mathematics) |
| Zdroj: | Studies in Applied Mathematics. 141:424-473 |
| ISSN: | 0022-2526 |
| DOI: | 10.1111/sapm.12229 |
| Popis: | The Askey–Wilson polynomials are a four-parameter family of orthogonal symmetric Laurent polynomials Rn[z] that are eigenfunctions of a second-order q-difference operator L, and of a second-order difference operator in the variable n with eigenvalue z + z−1 = 2x. Then, L and multiplication by z + z−1 generate the Askey–Wilson (Zhedanov) algebra. A nice property of the Askey–Wilson polynomials is that the variables z and n occur in the explicit expression in a similar and to some extent exchangeable way. This property is called duality. It returns in the nonsymmetric case and in the underlying algebraic structures: the Askey–Wilson algebra and the double affine Hecke algebra (DAHA). In this paper, we follow the degeneration of the Askey–Wilson polynomials until two arrows down and in four different situations: for the orthogonal polynomials themselves, for the degenerate Askey–Wilson algebras, for the nonsymmetric polynomials, and for the (degenerate) DAHA and its representations. |
| Databáze: | OpenAIRE |
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