论文信息 - 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

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.

Alexander Varchenko | A. Varchenko

[1] R. Askey. Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews , 1980 .

[2] V. Dotsenko,et al. Conformal Algebra and Multipoint Correlation Functions in 2d Statistical Models - Nucl. Phys. B240, 312 (1984) , 1984 .

[3] A. Varchenko. THE EULER BETA-FUNCTION, THE VANDERMONDE DETERMINANT, LEGENDRE'S EQUATION, AND CRITICAL VALUES OF LINEAR FUNCTIONS ON A CONFIGURATION OF HYPERPLANES. II , 1990 .

[4] A N Varchenko. Critical values and the determinant of the periods , 1989 .

[5] K. Aomoto. On the Structure of Integrals of Power Product of Linear Functions , 1977 .

[6] Gian-Carlo Rota,et al. The theory of Möbius functions , 1986 .

[7] Vadim Schechtman,et al. Arrangements of hyperplanes and Lie algebra homology , 1991 .

[8] P. Orlik,et al. Combinatorics and topology of complements of hyperplanes , 1980 .

[9] C. Sabbah,et al. Equations aux différences finies et déterminants d'intégrales de fonctions multiformes , 1991 .

[10] M. Gaudin. Diagonalisation d'une classe d'hamiltoniens de spin , 1976 .

[11] Vladimir E. Korepin,et al. Calculation of norms of Bethe wave functions , 1982 .

[12] K. Aomoto. ON THE COMPLEX SELBERG INTEGRAL , 1987 .

[13] V. Dotsenko,et al. Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge C≤1 , 1984 .

[14] Determinant formula for Selberg-type integrals , 1991 .