Path Model for Representations of Generalized Kac--Moody Algebras

TL;DR

This paper embeds Joseph-Lamprou's path model for generalized Kac-Moody algebra representations into Littelmann's model, enabling new decomposition and branching rules, and characterizes standard paths via a generalized Coxeter monoid.

Contribution

It introduces an embedding of Joseph-Lamprou's path model into Littelmann's model, leading to new structural insights and rules for generalized Kac-Moody algebra representations.

Findings

Embedded Joseph-Lamprou's path model into Littelmann's model

Derived tensor product decomposition rule for path crystals

Established a characterization of standard paths via a generalized Coxeter monoid

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.