%0 Journal Article
%T Path Model for Representations of Generalized Kac--Moody Algebras
%A Motohiro Ishii
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1112.3708v2