On the SO(<i>n</i> + 3) to SO(<i>n</i>) branching multiplicity space

Emilio A. Lauret; Fiorela Rossi Bertone

doi:10.1016/j.crma.2018.09.004

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)]

Présenté par : Michèle Vergne

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

Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1112-1124.

Résumé
Abstract

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 : 2018-08-25
Accepté le : 2018-09-11
Publié le : 2018-10-01

DOI : 10.1016/j.crma.2018.09.004

Affiliations des auteurs :

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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     author = {Emilio A. Lauret and Fiorela Rossi Bertone},
     title = {On the {SO(\protect\emph{n} + 3)} to {SO(\protect\emph{n})} branching multiplicity space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1112--1124},
     publisher = {Elsevier},
     volume = {356},
     number = {11-12},
     year = {2018},
     doi = {10.1016/j.crma.2018.09.004},
     language = {en},
}

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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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