Representations of Quantum Affine Algebras in their R-Matrix Realization

We use the isomorphisms between the R-matrix and Drinfeld presentations of the quantum affine algebras in types B, C and D produced in our previous work to describe finite-dimensional irreducible representations in the R-matrix realization.We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the R-matrix and Drinfeld presentations of the Yangians.

The Gauss decomposition of products of spherical harmonics

The product of two homogeneous harmonic polynomials is homogeneous, but not harmonic, in general. We give formulas for the Gauss decomposition of the product of two homogeneous harmonic polynomials.