Embeddings of Schur Functions into Types B/C/D

We consider the problem of embedding the semi-ring of Schur-positive symmetric polynomials into its analogue for the classical types B/C/D. If we preserve highest weights and add the additional Lie-theoretic parity assumption that the weights in images of Schur functions lie in a single translate of the root lattice, there are exactly two solutions. These naturally extend the Kirillov–Reshetikhin decompositions of representations of symplectic and orthogonal quantum affine algebras Uq( ).