Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with \(U_q (sl_n)\) at \(|q|=1\)

DOI10.2977/prims/1195143360zbMath0963.33006arXivmath/9905137OpenAlexW2115964611MaRDI QIDQ1577647

Yoshihiro Takeyama, Tetsuji Miwa, Vitaly O. Tarasov

Publication date: 17 June 2001

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9905137

zbMATH Keywords

quantum Knizhnik-Zamolodchikov equationvector representationhypergeometric solutionquantum algebra \(U_q(sl_n)\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (1)

Multiple gamma function, its \(q\)- and elliptic analogue.

Cites Work

• A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type
• The determinant of a hypergeometric periodic matrix
• Finite difference equations and determinants of integrals of multiform functions
• Arrangements of hyperplanes and Lie algebra homology
• Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras
• Quantization of the space of conformal blocks
• The Determinant of a Hypergeometric Period Matrix
• Arrangements d'hyperplans et sommes de Gauss
• Quantum KZ equation with |q| = 1 and correlation functions of theXXZmodel in the gapless regime
• Smirnov's integrals and the quantum Knizhnik-Zamolodchikov equation of level 0
• Quantum Knizhnik-Zamolodchikov equation for U_q(sl_n) and integral formula
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