Determinant Formula for Solutions of the Quantum Knizhnik–Zamolodchikov Equation Associated with $U_q(sl_n)$ at $|q| = 1$

Tetsuji Miwa; Yoshihiro Takeyama; Vitaly Tarasov

doi:10.2977/prims/1195143360

JournalsprimsVol. 35, No. 6pp. 871–892

Determinant Formula for Solutions of the Quantum Knizhnik–Zamolodchikov Equation Associated with $U_{q} (s l_{n})$ at $∣ q ∣ = 1$

Tetsuji Miwa
Kyoto University, Japan
Yoshihiro Takeyama
Kyoto University, Japan
Vitaly Tarasov
Steklov Mathematical Institute, St. Petersburg, Russian Federation

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Abstract

We construct the hypergeometric solutions for the quantized Knizhnik–Zamolodchikov equation with values in a tensor product of vector representations of $U_{q} (s l_{n})$ 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 $U_{q} (s l_{n})$ at $∣ q ∣ = 1$ . Publ. Res. Inst. Math. Sci. 35 (1999), no. 6, pp. 871–892

DOI 10.2977/PRIMS/1195143360