English

The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

Quantum Algebra 2009-01-27 v4 Representation Theory

Abstract

We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra glNgl_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

Cite

@article{arxiv.0810.2581,
  title  = {The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials},
  author = {Saburo Kakei and Michitomo Nishizawa and Yoshihisa Saito and Yoshihiro Takeyama},
  journal= {arXiv preprint arXiv:0810.2581},
  year   = {2009}
}

Comments

no figure, we gave a proof of the conjecture in the second version; we modified section 4.2 of the first version to correct an error in Proposition 4.4 and give more general result