A Combinatorial Model for Crystals of Kac-Moody Algebras
Representation Theory
2007-05-23 v4 Combinatorics
Abstract
We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a Littlewood-Richardson rule for decomposing tensor products of irreducible representations. The new model is based on the notion of a lambda-chain, which is a chain of positive roots defined by certain interlacing conditions.
Cite
@article{arxiv.math/0502147,
title = {A Combinatorial Model for Crystals of Kac-Moody Algebras},
author = {Cristian Lenart and Alexander Postnikov},
journal= {arXiv preprint arXiv:math/0502147},
year = {2007}
}
Comments
28 pages, 2 figures