Determinant formula for the solution of the quantum Knizhnik-Zamolodchikov equation with \(|q|=1\). (English) Zbl 0953.81037
Jing, Naihuan (ed.) et al., Recent developments in quantum affine algebras and related topics. Proceedings of the international conference on representations of affine and quantum affine algebras and their applications, North Carolina State University, Raleigh, NC, USA, May 21-24, 1998. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 248, 377-393 (1999).
The authors construct the fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with \(U_q(\widehat{sl}_2)\) for \(|q|=1\) and give a formula for its determinant in terms of double sine functions. The solution itself is constructed in terms of \(l\)-dimensional integrals and the non-degeneracy of the matrix is proven by computing its determinant. The integrands of the integrals are meromorphic functions given explicitly in terms of double sine functions and the determinant itself is a simple product of double sine functions.
For the entire collection see [Zbl 0932.00043].
For the entire collection see [Zbl 0932.00043].
Reviewer: Volodymyr Mazorchuk (Kyïv)
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 32G34 | Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 82B23 | Exactly solvable models; Bethe ansatz |
