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arXiv:0907.1336 [math.RT]AbstractReferencesReviewsResources

Pieri algebras for the orthogonal and symplectic groups

Sangjib Kim, Soo Teck Lee

Published 2009-07-08, updated 2010-03-18Version 2

We study the structure of a family of algebras which encodes a generalization of the Pieri Rule for the complex orthogonal group. In particular, we show that each of these algebras has a standard monomial basis and has a flat deformation to a Hibi algebra. There is also a parallel theory for the complex symplectic group.

Comments: 26 pages, v2: new introduction, improved exposition, examples.
Categories: math.RT, math.CO
Subjects: 20G05, 05E15
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