  Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie
algebra. A family of central elements or Casimir invariants are constructed and
their eigenvalues computed in any integrable irreducible highest weight
representation. These eigenvalue formulae are shown to absolutely convergent
when the deformation parameter $q$ is such that $|q|>1$. 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, the braid generator is shown to be diagonalizable on arbitrary
tensor product modules of integrable irreducible highest weight $U_q(\hat{\cal
G})$-modules and a spectral decomposition formula for the braid generator is
obtained which is the generalization of Reshetikhin's and Gould's forms to the
present affine case. Casimir invariants acting on a specified module are also
constructed and their eigenvalues, again absolutely convergent for $|q|>1$,
computed by means of the spectral decomposition formula.
