q-Difference Systems for the Jackson Integral of Symmetric Selberg Type
We provide an explicit expression for the first-order -difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of the -analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system, we use a set of symmetri...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| ISSN: | 1815-0659 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211007 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type. Masahiko Ito. SIGMA 16 (2020), 113, 31 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We provide an explicit expression for the first-order -difference system for the Jackson integral of symmetric Selberg type. The q-difference system gives a generalization of the -analog of contiguous relations for the Gauss hypergeometric function. As a basis of the system, we use a set of symmetric polynomials introduced by Matsuo in his study of the -KZ equation. Our main result is an explicit expression for the coefficient matrix of the -difference system in terms of its Gauss matrix decomposition. We introduce a class of symmetric polynomials called interpolation polynomials, which includes Matsuo's polynomials. By repeated use of three-term relations among the interpolation polynomials, we compute the coefficient matrix.
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| ISSN: | 1815-0659 |