Embeddings of Schur functions into types B/C/D

Abstract

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).