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.
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@article{CRMATH_2010__348_17-18_959_0, author = {Zhu, Fuhai and Liang, Ke}, title = {On a branching law of unitary representations and a conjecture of {Kobayashi}}, journal = {Comptes Rendus. Math\'ematique}, pages = {959--962}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.09.006}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.09.006/} }
TY - JOUR AU - Zhu, Fuhai AU - Liang, Ke TI - On a branching law of unitary representations and a conjecture of Kobayashi JO - Comptes Rendus. Mathématique PY - 2010 SP - 959 EP - 962 VL - 348 IS - 17-18 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.09.006/ DO - 10.1016/j.crma.2010.09.006 LA - en ID - CRMATH_2010__348_17-18_959_0 ER -
%0 Journal Article %A Zhu, Fuhai %A Liang, Ke %T On a branching law of unitary representations and a conjecture of Kobayashi %J Comptes Rendus. Mathématique %D 2010 %P 959-962 %V 348 %N 17-18 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.09.006/ %R 10.1016/j.crma.2010.09.006 %G en %F CRMATH_2010__348_17-18_959_0
Zhu, Fuhai; Liang, Ke. On a branching law of unitary representations and a conjecture of Kobayashi. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 959-962. doi : 10.1016/j.crma.2010.09.006. http://archive.numdam.org/articles/10.1016/j.crma.2010.09.006/
[1] M. Duflo, J. Vargas, Proper maps and multiplicities, preprint.
[2] The restriction of to reductive subgroups, Proc. Japan Acad., Volume 69 (1993), pp. 262-267
[3] Discrete decomposability of the restriction of with respect to reductive subgroups and its applications, Invent. Math., Volume 117 (1994), pp. 181-205
[4] Discrete decomposability of the restriction of , Part III: Restriction of Harish–Chandra modules and associated varieties, Invent. Math., Volume 131 (1998), pp. 229-256
[5] 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] 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] Branching problems of unitary representations, Proceedings of the International Congress of Mathematicians, vol. II, Higher Ed. Press, Beijing, 2002, pp. 615-627
[8] 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] 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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