Path Model for Representations of Generalized Kac--Moody Algebras
Representation Theory
2013-04-16 v2 Combinatorics
Quantum Algebra
Abstract
We show that Joseph-Lamprou's path model for representations of generalized Kac-Moody algebras can be embedded into Littelmann's path model for certain Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals, we give a decomposition rule for tensor product and a branching rule for restriction to Levi subalgebras. Also, we obtain a characterization of standard paths in terms of a certain monoid, which can be thought of as a generalization of a Coxeter group.
Keywords
Cite
@article{arxiv.1112.3708,
title = {Path Model for Representations of Generalized Kac--Moody Algebras},
author = {Motohiro Ishii},
journal= {arXiv preprint arXiv:1112.3708},
year = {2013}
}
Comments
30 pages