Embeddings of Schur functions into types B/C/D

2000/09/21 by Michael Kleber, Kleber, Michael
Mathematics · #05E05 (Primary) 17B10 #17B37(Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.QA #math.RT #msc:05E05 #msc:17B10

paper · pdf · doi:10.48550/arxiv.math/0009199

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

arxiv created 2000/10/05 · arxiv updated 2009/11/30

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(g) (some still conjectural, some recently proven).

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