no. G10
Article de recherche - Théorie des représentations
Multiplicities of Representations in Algebraic Families
[Multiplicités des représentations dans les familles algébriques]
Cai, Li1 ; Fan, Yangyu2 
1Academy for Multidisciplinary Studies, Beijing National Center for Applied Mathematics, Capital Normal University, Beijing, 100048, People’s Republic of China
2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Comptes Rendus. Mathématique, Tome 362 (2024) no. G10, pp. 1097-1107

In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally constancy of Euler–Poincaré numbers. This generalizes the main result of Aizenbud–Sayag for unramified twisting families.

Dans cette courte note, nous considérons les multiplicités de représentations dans des familles algébriques générales,en particulier la semi-continuité supérieure des multiplicités homologiques et la constance locale des nombres d’Euler–Poincaré. Ceci généralise le résultat principal d’Aizenbud–Sayag pour les familles obtenues en induisant une représentation fixée que l’on tord par des caractères non ramifiés.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/crmath.623
Classification : 22E45, 20G25
Keywords: Branching laws, Homological multiplicities, Spherical varieties
Mots-clés : Lois de branchement, multiplicités homologiques, variétés sphériques

Cai, Li  1   ; Fan, Yangyu  2

1 Academy for Multidisciplinary Studies, Beijing National Center for Applied Mathematics, Capital Normal University, Beijing, 100048, People’s Republic of China
2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Cai, Li; Fan, Yangyu. Multiplicities of Representations in Algebraic Families. Comptes Rendus. Mathématique, Tome 362 (2024) no. G10, pp. 1097-1107. doi: 10.5802/crmath.623

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