# Determinant Formula for Solutions of the Quantum Knizhnik–Zamolodchikov Equation Associated with <em>U<sub>q</sub></em>(<em>sl<sub>n</sub></em>) at |<em>q</em>| = 1

### Tetsuji Miwa

Kyoto University, Japan### Yoshihiro Takeyama

Kyoto University, Japan### Vitaly Tarasov

Steklov Mathematical Institute, St. Petersburg, Russian Federation

## Abstract

We construct the hypergeometric solutions for the quantized Knizhnik–Zamolodchikov equation with values in a tensor product of vector representations of *Uq*(*sln*) at |*q*| = 1 and give an explicit formula for the corresponding determinant in terms of the double sine function.

## Cite this article

Tetsuji Miwa, Yoshihiro Takeyama, Vitaly Tarasov, Determinant Formula for Solutions of the Quantum Knizhnik–Zamolodchikov Equation Associated with <em>U<sub>q</sub></em>(<em>sl<sub>n</sub></em>) at |<em>q</em>| = 1. Publ. Res. Inst. Math. Sci. 35 (1999), no. 6, pp. 871–892

DOI 10.2977/PRIMS/1195143360