Comptes Rendus
no. 17-18
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]
Présenté par : Michel Duflo
Fuhai Zhu1 ; Ke Liang1
1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 959-962

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.

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.

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

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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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