The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra glN. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We p...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2009 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149247 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials / S. Kakei, M. Nishizawa, Y. Saito, Y. Takeyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730928248324096 |
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| author | Kakei, S. Nishizawa, M. Saito, Y. Takeyama, Y. |
| author_facet | Kakei, S. Nishizawa, M. Saito, Y. Takeyama, Y. |
| citation_txt | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials / S. Kakei, M. Nishizawa, Y. Saito, Y. Takeyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra glN. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We prove that our solutions contain those obtained as a scaling limit of matrix elements of the vertex operators of level one.
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| first_indexed | 2025-12-07T19:23:52Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149247 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:23:52Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kakei, S. Nishizawa, M. Saito, Y. Takeyama, Y. 2019-02-19T19:18:43Z 2019-02-19T19:18:43Z 2009 The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials / S. Kakei, M. Nishizawa, Y. Saito, Y. Takeyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 16 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 39A13; 33C52; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/149247 We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra glN. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We prove that our solutions contain those obtained as a scaling limit of matrix elements of the vertex operators of level one. This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. Research of SK is supported by Grant-in-Aid for Scientific Research (C) No. 19540228. Research of MN is supported by Grant-in-Aid for Young Scientists (B) No. 18749001. Research of YS is supported by Grant-in-Aid for Scientific Research (C) No. 20540009. Research of YT is supported by Grant-in-Aid for Young Scientists (B) No. 20740088. The authors thank Takeshi Suzuki for helpful discussions. They are also deeply grateful to Charles Dunkl for valuable comments and pointing out an error in Section 4.2 of the earlier draft. YT thanks Takeshi Ikeda, Masahiro Kasatani and Hiroshi Naruse for discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials Article published earlier |
| spellingShingle | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials Kakei, S. Nishizawa, M. Saito, Y. Takeyama, Y. |
| title | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials |
| title_full | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials |
| title_fullStr | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials |
| title_full_unstemmed | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials |
| title_short | The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials |
| title_sort | rational qkz equation and shifted non-symmetric jack polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149247 |
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