GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES

The general formula for the universal R-matrix for quantified nontwist ed affine algebras, obtained by the first and third authors, is applie d to zero central charge, highest weight modules of the quantized affi ne algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tenser product of these mo dules. In particular, A(1)((1)) current realization of the universal R -matrix is presented. It gives a new universal presentation for the tr igonometric R-matrix with a parameter in tenser product of U-q(sl(2))- Verma modules. Detailed analysis of a scalar factor arising in finite- dimensional representations of the universal R-matrix for any U-q(g) i s 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.