Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz

1994/11/24 by V. Tarasov, Tarasov, V., Alexander Varchenko +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9411181

6 pages, amstex.tex (ver 2.1), amsppt.sty (ver 2.1)

arxiv created 1994/11/24 · openalex publication_date 1994/11/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an integral representation for solutions to the quantized Knizhnik- Zamolodchikov equation (qKZ) associated with the Lie algebra gl_N+1. Asymptotic solutions to qKZ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum spin chain model. We show that the norm of the Bethe vector is equal to the product of the Hessian of a suitable function and an explicitly written rational function. This formula is a generalization of the Gaudin-Korepin formula for a norm of the Bethe vector. We show that, generically, the Bethe vectors form a base for the gl₂ case.

Citations

• Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors

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