Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation

Abstract

We construct Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation for $U_q({\widehat{\mathfrak{sl}}}_2)$ on the parabolic Kazhdan--Lusztig bases. They are characterized by non-symmetric Koornwinder polynomials with the specialized parameters. As a special case, we obtain the solution of the minimal degree.

arXiv comment22 pages

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