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Lie群論・表現論セミナー
過去の記録 ～05/02｜次回の予定｜今後の予定 05/03～
| 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 |
2024年11月12日(火)
17:30-18:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同
井上順子 氏 (鳥取大学)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
トポロジー火曜セミナーと合同
井上順子 氏 (鳥取大学)
Holomorphically induced representations of some solvable Lie groups
(Japanese )
[ 講演概要 ]
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
From a viewpoint of the orbit method, holomorphic induction is originally based on the idea of realizing an irreducible unitary representation of a Lie group $G$ in an $L^2$-space of some holomorphic sections of some line bundle over a $G$-homogeneous space associated with a polarization for a linear form of the Lie algebra of $G$. It is a generalization of ordinary induction from a unitary character; Through this process, Auslander-Kostant constructed the irreducible unitary representations of type 1, connected, simply connected solvable Lie groups.
In this talk, focusing on the class of exponential solvable Lie groups, we are concerned with holomorphically induced representations $\rho$ in some general settings.
We would like to discuss the following problems:
(1) conditions of non-vanishing of $\rho$,
(2) decomposition of $\rho$ into a direct integral of irreducible representations,
(3) Frobenius reciprocity in the sense of Penney distributions.
