Macdonald Polynomials and Multivariable Basic Hypergeometric Series
We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147804 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Macdonald Polynomials and Multivariable Basic Hypergeometric Series / M.J. Schlosser // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 55 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719929153748992 |
|---|---|
| author | Schlosser, M.J. |
| author_facet | Schlosser, M.J. |
| citation_txt | Macdonald Polynomials and Multivariable Basic Hypergeometric Series / M.J. Schlosser // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 55 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6φ5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8φ7 summation. Motivated by our basic hypergeometric analysis, we propose an extension of Macdonald polynomials to Macdonald symmetric functions indexed by partitions with complex parts. These appear to possess nice properties.
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| first_indexed | 2025-12-07T18:23:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147804 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:23:00Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Schlosser, M.J. 2019-02-16T08:31:56Z 2019-02-16T08:31:56Z 2007 Macdonald Polynomials and Multivariable Basic Hypergeometric Series / M.J. Schlosser // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 55 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D52; 15A09; 33D67 https://nasplib.isofts.kiev.ua/handle/123456789/147804 We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6φ5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8φ7 summation. Motivated by our basic hypergeometric analysis, we propose an extension of Macdonald polynomials to Macdonald symmetric functions indexed by partitions with complex parts. These appear to possess nice properties. This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. I would like to thank Michel Lassalle for getting me involved into Macdonald polynomials (especially concerning the issues related to matrix inversion and explicit expressions) and his encouragement. I would also like to express my sincere gratitude to the organizers of the “Workshop on Jack, Hall–Littlewood and Macdonald Polynomials” (ICMS, Edinburgh, September 23–26, 2003) for inviting me to participate in that very stimulating workshop. Among them, I am especially indebted to Vadim Kuznetsov whose interest in explicit formulae for Macdonald polynomials served as an inspiration for the present work. The author was partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Macdonald Polynomials and Multivariable Basic Hypergeometric Series Article published earlier |
| spellingShingle | Macdonald Polynomials and Multivariable Basic Hypergeometric Series Schlosser, M.J. |
| title | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
| title_full | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
| title_fullStr | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
| title_full_unstemmed | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
| title_short | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
| title_sort | macdonald polynomials and multivariable basic hypergeometric series |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147804 |
| work_keys_str_mv | AT schlossermj macdonaldpolynomialsandmultivariablebasichypergeometricseries |