Lie群論・表現論セミナー

過去の記録 ~10/17次回の予定今後の予定 10/18~

開催情報 火曜日 16:30~18:00 数理科学研究科棟(駒場) 126号室
担当者 小林俊行
セミナーURL https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

次回の予定

2019年10月23日(水)

16:30-18:00   数理科学研究科棟(駒場) 128号室
Clemens Weiske 氏 (Aarhus University)
Symmetry breaking and unitary branching laws for finite-multiplicity pairs of rank one (English)
[ 講演概要 ]
Let (G,G’) be a real reductive finite multiplicity pair of rank one, i.e. a rank one real reductive group G with reductive subgroup G’, such that the space of symmetry breaking operators (SBOs) between all (smooth admissible) irreducible representations is finite dimensional.

We give a classification of SBOs between spherical principal series representations of G and G’, essentially generalizing the results on (O(1,n+1),O(1,n)) of Kobayashi—Speh (2015). Moreover we show how to decompose unitary representations occurring in (not necessarily) spherical principal series representations of G in terms of unitary G’ representations, by making use of the knowledge gathered in the classification of the SBOs and the structure of the open P’orbit in G/P as a homogenous G’-space, where P’ is a minimal parabolic in G’ and P is a minimal parabolic in G. This includes the construction of discrete spectra in the restriction of complementary series representations and unitarizable composition factors.