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Article Dans Une Revue International Mathematics Research Notices Année : 2022

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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Dates et versions

hal-03235536 , version 1 (25-05-2021)
hal-03235536 , version 2 (08-04-2022)

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Pierre-Emmanuel Chaput, Nicolas Ressayre. Reduction for branching multiplicities. International Mathematics Research Notices, 2022, ⟨10.1093/imrn/rnac248⟩. ⟨hal-03235536v2⟩
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