Bilinear Identity for q-Hypergeometric Integrals

We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also gives an explicit formula for scalar products of solutions of the qKZ and the dual qKZ equations, therefore providing a deformation of Gaudin-Korepin's formula for norms of the Bethe vectors.Comment: 18 pages, amstex.tex (ver. 2.1) and amssym.tex are required; misprints are correcte

On Irreducibility of Tensor Products of Yangian Modules

We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.Comment: 21 pages, AmS-Te