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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| Veröffentlicht in: | Symmetry, integrability and geometry, methods and applications Jg. 3; S. 056 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Kiev
National Academy of Sciences of Ukraine
01.01.2007
National Academy of Science of Ukraine |
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| ISSN: | 1815-0659, 1815-0659 |
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| Abstract | 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 6?5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8?7 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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| AbstractList | 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 6?5 summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised 8?7 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. 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 _6phi_5$ summation formula. We derive several new related identities including multivariate extensions of Jackson's very-well-poised _8phi_7$ 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. |
| Author | Schlosser, Michael J. |
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| Copyright | Copyright National Academy of Sciences of Ukraine 2007 |
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| DOI | 10.3842/SIGMA.2007.056 |
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| Title | Macdonald Polynomials and Multivariable Basic Hypergeometric Series |
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