The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

Details The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials

2008-10-15

arxiv.org/abs/0810.2581v4

SIGMA 5 (2009), 010, 12 pages

Mathematics

Quantum Algebra

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

Scientific paper

10.3842/SIGMA.2009.010

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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