Pieri algebras for the orthogonal and symplectic groups
Representation Theory
2010-03-19 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.0907.1336,
title = {Pieri algebras for the orthogonal and symplectic groups},
author = {Sangjib Kim and Soo Teck Lee},
journal= {arXiv preprint arXiv:0907.1336},
year = {2010}
}
Comments
26 pages, v2: new introduction, improved exposition, examples.