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 tenser product of sh representations are considered . The first term of asymptotics is an eigenvector of a system of commu ting operators. We show that the norm of this vector with respect to t he 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.