Reduction for branching multiplicities
Résumé
A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in [KT03, DW11]. This formula holds when the highest weights of the representations belong to a codimension 1 face of the Horn cone, which by [Res11b] corresponds to a Littlewood-Richardson coefficient equal to 1. We prove a similar reduction formula when this coefficient is equal to 2, and show some properties of the class of the branch divisor corresponding to a generically finite morphism of degree 2 naturally defined in this context.
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Commentaire : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing)
Commentaire : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing)