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Factorization of Schur functions of various types

✍ Scribed by Hiroshi Mizukawa


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
197 KB
Volume
269
Category
Article
ISSN
0021-8693

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✦ Synopsis


In his book [The Theory of Group Characters, 2nd edition, Clarendon, Oxford, 1950], D.E. Littlewood showed that, under certain change of variables, the Schur function factorizes into those indexed by the quotient of the partition. In this paper we discuss the factorization of Schur functions of various classical groups.


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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