QUANTIZED AFFINE LIE-ALGEBRAS AND DIAGONALIZATION OF BRAID GENERATORS

Let U(q)(G) be a quantized affine Lie algebra. It is proven that the u niversal R-matrix R of U(q)(G) satisfies the celebrated conjugation re lation R(dagger) = TR with T the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor pro duct modules of integrable irreducible highest weight U(q)(G)-module a nd a spectral decomposition formula for the braid generator is obtaine d which is the generalization of Reshetikhin and Gould forms to the pr esent affine case. Casimir invariants are constructed and their eigenv alues computed by means of the spectral decomposition formula. As a by -product, an interesting identity is found.