Comptes Rendus
Lie algebras
On the SO(n + 3) to SO(n) branching multiplicity space
[Sur l'espace de multiplicité de branchement de SO(n + 3) vers SO(n)]
Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1112-1124.

Nous étudions la décomposition de l'espace de multiplicité, comme SO(3)-module, correspondant au branchement de SO(n+3) vers SO(n). Ici, SO(n) (resp. SO(3)) est considéré comme plongé dans SO(n+3) dans le bloc en haut à gauche (resp. le bloc en bas à droite). Nous montrons que, lorsque le plus grand poids de la représentation irréductible de SO(n) s'entrelace avec le plus grand poids de la représentation irréductible de SO(n+3), alors l'espace de multiplicité se décompose en un produit tensoriel de (n+2)/2 représentations réductibles de SO(3).

We study the decomposition as an SO(3)-module of the multiplicity space corresponding to the branching from SO(n+3) to SO(n). Here, SO(n) (resp. SO(3)) is considered embedded in SO(n+3) in the upper left-hand block (resp. lower right-hand block). We show that when the highest weight of the irreducible representation of SO(n) interlaces the highest weight of the irreducible representation of SO(n+3), then the multiplicity space decomposes as a tensor product of (n+2)/2 reducible representations of SO(3).

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2018.09.004

Emilio A. Lauret 1 ; Fiorela Rossi Bertone 1

1 CIEM–FaMAF (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina
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     title = {On the {SO(\protect\emph{n} + 3)} to {SO(\protect\emph{n})} branching multiplicity space},
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Emilio A. Lauret; Fiorela Rossi Bertone. On the SO(n + 3) to SO(n) branching multiplicity space. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1112-1124. doi : 10.1016/j.crma.2018.09.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.09.004/

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This research was partially supported by grants from CONICET and Agencia Nacional de Promoción Científica y Tecnológica (PICT-2015-0274 and PICT-2014-2706). The first named author was supported by the Alexander von Humboldt Foundation.

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