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Macdonald Polynomials and Multivariable Basic Hypergeometric Series
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Macdonald Polynomials and Multivariable Basic Hypergeometric Series
Інший ID:
2000 Mathematics Subject Classification: 33D52; 15A09; 33D67
Посилання:
Macdonald Polynomials and Multivariable Basic Hypergeometric Series / M.J. Schlosser // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 55 назв. — англ.
Підтримка:
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”).
Дата:
2007
Переглядів:
626
Завантажень:
236
Анотація:
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.
