GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES

Abstract

The general formula for the universal R-matrix for quantized nontwisted affine algebras, obtained by the first and third authors, is applied to zero central charge, highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tensor product of these modules. In particular, [Formula: see text] current realization of the universal R-matrix is presented. It gives a new universal presentation for the trigonometric R-matrix with a parameter in tensor product of Uq(sl2)-Verma modules. Detailed analysis of a scalar factor arising in finite-dimensional representations of the universal R-matrix for any Uq(ĝ) is given. We interpret this scalar factor as a multiplicative bilinear form on highest weight polynomials of irreducible representations and express this form in terms of infinite q-shifted factorials.