Composantes PRV g\'en\'eralis\'ees et chemins de Littelmann

TL;DR

This paper provides a sufficient condition for Littelmann paths to represent extremal weight vectors in integrable highest weight representations of symmetrizable Kac-Moody algebras, offering an alternative proof for generalized PRV components.

Contribution

It introduces a new sufficient condition for Littelmann paths to correspond to extremal weights, generalizing previous results and simplifying proofs.

Findings

Established a sufficient condition for extremal weight representation

Provided an alternative proof for the existence of generalized PRV components

Extended the context of previous results to more general settings

Abstract

We give a sufficient condition for a Littelmann path to represent a vector of extremal weight of an integrable irreducible highest weight representation of a symmetrisable Kac-Moody algebra. Thanks to this condition we present, in a more general context, an alternative proof of recent result by Boris Pasquier, Nicolas Ressayre and the author of this article on the existence of generalized PRV components.