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: Kakei, S., Nishizawa, M., Saito, Y., Takeyama, Y.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
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
id nasplib_isofts_kiev_ua-123456789-149247
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
spellingShingle The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
Kakei, S.
Nishizawa, M.
Saito, Y.
Takeyama, Y.
title_short 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_sort rational qkz equation and shifted non-symmetric jack polynomials
author Kakei, S.
Nishizawa, M.
Saito, Y.
Takeyama, Y.
author_facet Kakei, S.
Nishizawa, M.
Saito, Y.
Takeyama, Y.
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149247
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.
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