  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 $U_q(\hat{g})$ (some still conjectural, some
recently proven).
