Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito, Yoshihiro Takeyama, “The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials”, SIGMA, 2009, Volume 5,010, 12 pp.

This article is cited in 2 papers

The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

Saburo Kakei^a, Michitomo Nishizawa^b, Yoshihisa Saito^c, Yoshihiro Takeyama^d

^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

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.

MSC: 39A13; 33C52; 81R50

Received: October 15, 2008; in final form January 15, 2009; Published online January 27, 2009

Language: English

DOI: 10.3842/SIGMA.2009.010