  Let $U_q(\hat{\cal G})$ be a quantized affine Lie algebra. It is proven that
the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated
conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As
applications, braid generators are shown to be diagonalizable on arbitrary
tensor product modules of integrable irreducible highest weight $U_q(\hat{\cal
G})$-module and a spectral decomposition formula for the braid generators is
obtained which is the generalization of Reshetikhin's and Gould's forms to the
present affine case. Casimir invariants are constructed and their eigenvalues
computed by means of the spectral decomposition formula. As a by-product, an
interesting identity is found.
