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.

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/

[1] M. Duflo, J. Vargas, Proper maps and multiplicities, preprint.

[2] T. Kobayashi The restriction of Aq(λ) to reductive subgroups, Proc. Japan Acad., Volume 69 (1993), pp. 262-267

[3] T. Kobayashi Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups and its applications, Invent. Math., Volume 117 (1994), pp. 181-205

[4] T. Kobayashi Discrete decomposability of the restriction of Aq(λ), Part III: Restriction of Harish–Chandra modules and associated varieties, Invent. Math., Volume 131 (1998), pp. 229-256

[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

  • Masatoshi Kitagawa Kobayashi’s Conjectures on the Discrete Decomposability, Symmetry in Geometry and Analysis, Volume 3, Volume 359 (2025), p. 31 | DOI:10.1007/978-981-97-7666-5_3
  • Toshiyuki Kobayashi Recent advances in branching problems of representations, Sugaku Expositions, Volume 37 (2024) no. 2, pp. 129-177 | DOI:10.1090/suga/485 | Zbl:7989018
  • Michel Duflo; Esther Galina; Jorge A. Vargas Square integrable representations of reductive Lie groups with admissible restriction to SL2(R), Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1033-1056 | Zbl:1385.22004
  • Toshiyuki Kobayashi A program for branching problems in the representation theory of real reductive groups, Representations of Reductive Groups, Volume 312 (2015), p. 277 | DOI:10.1007/978-3-319-23443-4_10

Cité par 4 documents. Sources : Crossref, zbMATH

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