Symmetry, Integrability and Geometry: Methods and Applications (Jan 2009)

The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

  • Saburo Kakei,
  • Michitomo Nishizawa,
  • Yoshihisa Saito,
  • Yoshihiro Takeyama

Journal volume & issue
Vol. 5
p. 010

Abstract

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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.

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