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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 010, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.010 (Mi sigma356) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

Saburo Kakeia, Michitomo Nishizawab, Yoshihisa Saitoc, Yoshihiro Takeyamad

a Department of Mathematics, College of Science, Rikkyo University, Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan
b Department of Mathematics, Faculty of Education, Hirosaki University, 1 Bunkyo-cho, Hirosaki, Aomori 036-8560, Japan
c Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan
d Department of Mathematics, Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
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DOI: https://doi.org/10.3842/SIGMA.2009.010
Abstract: We construct special solutions to the rational quantum Knizhnik–Zamolodchikov equation associated with the Lie algebra $gl_N$. 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.
Keywords: qKZ equation; shifted Jack polynomial; degenerate double affine Hecke algebra.
Received: October 15, 2008; in final form January 15, 2009; Published online January 27, 2009
Bibliographic databases:
Document Type: Article
MSC: 39A13; 33C52; 81R50
Language: English
Citation: Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito, Yoshihiro Takeyama, “The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials”, SIGMA, 5 (2009), 010, 12 pp.
Citation in format AMSBIB
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\by Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito, Yoshihiro Takeyama
\paper The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
\jour SIGMA
\yr 2009
\vol 5
\papernumber 010
\totalpages 12
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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