The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

Abstract

We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra $g{l}_N$. 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.

arXiv commentno 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

References in corpus (5)

• Symmetric and non-symmetric quantum Capelli polynomials
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Singular Polynomials and Modules for the Symmetric Groups
• Singular polynomials for the symmetric groups
• Rational and trigonometric degeneration of the double affine Hecke algebra of type $A$

Cited by in corpus (2)

• Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
• Computing nonsymmetric and interpolation Macdonald polynomials