Embeddings of Schur functions into types B/C/D

Details Embeddings of Schur functions into types B/C/D Embeddings of Schur functions into types B/C/D

2000-09-21

arxiv.org/abs/math/0009199v2

Mathematics

Combinatorics

13 pages. Minor changes only. Submitted to Journal of Algebra. "This work has been submitted to Academic Press for possible pu

Scientific paper

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).

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