Comptes Rendus
Lie Algebras/Harmonic Analysis
On a branching law of unitary representations and a conjecture of Kobayashi
[Sur une loi de branchement des représentations unitaires et une conjecture de Kobayashi]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 959-962.

Dans cette Note, nous considérons l'équivalence de différentes propriétés de la restriction d'une représentation unitaire irréductible d'un groupe de Lie réel réductif á un sous-groupe réductif fermé. Comme corollaire, nous prouvons une forme faible d'une conjecture de Kobayashi.

In this Note we consider the equivalence of different properties of the restriction of an irreducible unitary representation of a real reductive group to a closed reductive subgroup. As a corollary, we prove a weak form of a conjecture of Kobayashi.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.006

Fuhai Zhu 1 ; Ke Liang 1

1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
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Fuhai Zhu; Ke Liang. On a branching law of unitary representations and a conjecture of Kobayashi. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 959-962. doi : 10.1016/j.crma.2010.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.006/

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[5] T. Kobayashi Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups, J. Funct. Anal., Volume 152 (1998), pp. 100-135

[6] T. Kobayashi Discrete decomposable restrictions of unitary representations of reductive Lie groups–examples and conjectures, Okayama–Kyoto, 1997 (Adv. Stud. Pure Math.), Volume vol. 26, Math. Soc. Japan, Tokyo (2000), pp. 99-127

[7] T. Kobayashi Branching problems of unitary representations, Proceedings of the International Congress of Mathematicians, vol. II, Higher Ed. Press, Beijing, 2002, pp. 615-627

[8] T. Kobayashi Restrictions of unitary representations of real reductive groups, Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, Progr. Math., vol. 29, Birkhäuser Boston, Boston, MA, 2005, pp. 139-207

[9] B. Kostant On the tensor product of a finite and an infinite dimensional representation, J. Funct. Anal., Volume 20 (1975), pp. 257-285

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