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

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

1993-12-14

arxiv.org/abs/hep-th/9312119v1

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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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