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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211007 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type. Masahiko Ito. SIGMA 16 (2020), 113, 31 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862664748630278144 |
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| author | Ito, Masahiko |
| author_facet | Ito, Masahiko |
| citation_txt | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type. Masahiko Ito. SIGMA 16 (2020), 113, 31 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-16T07:30:58Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211007 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T07:30:58Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ito, Masahiko 2025-12-22T09:25:02Z 2020 q-Difference Systems for the Jackson Integral of Symmetric Selberg Type. Masahiko Ito. SIGMA 16 (2020), 113, 31 pages 1815-0659 2020 Mathematics Subject Classification: 33D60; 39A13 arXiv:1910.08393 https://nasplib.isofts.kiev.ua/handle/123456789/211007 https://doi.org/10.3842/SIGMA.2020.113 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. The author would like to thank the anonymous referees who kindly provided many careful comments and suggestions for improving his manuscript. He would also like to express his gratitude to Professor Peter J. Forrester for providing considerable encouragement from the early stage of this research. The comments and suggestions by Professor Yasuhiko Yamada on the preliminary version of this manuscript are most appreciated. This work was supported by JSPS KAKENHI Grant Number (C)18K03339. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications q-Difference Systems for the Jackson Integral of Symmetric Selberg Type Article published earlier |
| spellingShingle | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type Ito, Masahiko |
| title | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type |
| title_full | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type |
| title_fullStr | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type |
| title_full_unstemmed | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type |
| title_short | q-Difference Systems for the Jackson Integral of Symmetric Selberg Type |
| title_sort | q-difference systems for the jackson integral of symmetric selberg type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211007 |
| work_keys_str_mv | AT itomasahiko qdifferencesystemsforthejacksonintegralofsymmetricselbergtype |