Path Model for Representations of Generalized Kac--Moody Algebras

Details Path Model for Representations of Generalized Kac--Moody Algebras Path Model for Representations of Generalized Kac--Moody Algebras

2011-12-16

arxiv.org/abs/1112.3708v1

Mathematics

Representation Theory

30 pages

Scientific paper

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.

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