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

1993/12/14 by Alexander Varchenko, Varchenko, Alexander · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9312119

15 pages, no figures, posted by Pavel Etingof by the author's request

arxiv created 1993/12/14 · arxiv updated 2009/11/30

Abstract

The quasiclassical asymptotics of the Knizhnik-Zamolodchikov equation with values in the tensor product of sl(2)- representations are considered. The first term of asymptotics is an eigenvector of a system of commuting operators. We show that the norm of this vector with respect to the Shapovalov form is equal to the determinant of the matrix of second derivatives of a suitable function. This formula is an analog of the Gaudin and Korepin formulae for the norm of the Bethe vectors. We show that the eigenvectors form a basis under certain conditions.

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

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