Multiplicities of Representations in Algebraic Families

Li Cai; Yangyu Fan

doi:10.5802/crmath.623

Article de recherche - Théorie des représentations

Multiplicities of Representations in Algebraic Families
[Multiplicités des représentations dans les familles algébriques]

Li Cai ¹ ; Yangyu Fan 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

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1097-1107.

Résumé
Abstract

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.

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.

Reçu le : 2023-09-06
Révisé le : 2024-02-07
Accepté le : 2024-02-07
Publié le : 2024-11-05

DOI : 10.5802/crmath.623

Classification : 22E45, 20G25
Keywords: Branching laws, Homological multiplicities, Spherical varieties
Mots-clés : Lois de branchement, multiplicités homologiques, variétés sphériques

Affiliations des auteurs :

Li Cai ¹ ; Yangyu Fan 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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     author = {Li Cai and Yangyu Fan},
     title = {Multiplicities of {Representations} in {Algebraic} {Families}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1097--1107},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.623},
     language = {en},
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Li Cai; Yangyu Fan. Multiplicities of Representations in Algebraic Families. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1097-1107. doi : 10.5802/crmath.623. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.623/

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