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Lie群論・表現論セミナー
過去の記録 ～05/27｜次回の予定｜今後の予定 05/28～
| 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 |
2013年10月22日(火)
17:00-18:00 数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Louisiana State University (USA))
Representation Theory and Microlocal Analysis (ENGLISH)
Benjamin Harris 氏 (Louisiana State University (USA))
Representation Theory and Microlocal Analysis (ENGLISH)
[ 講演概要 ]
Suppose HsubsetK are compact, connected Lie groups, and suppose tau is an irreducible, unitary representation of H. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of IndKHtau by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on K. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation pi of a reductive Lie group G when restricted to a reductive subgroup H. One of his key ideas was to restrict pi to a representation of a maximal compact subgroup KsubsetG, view pi as a subrepresentation of L2(K), and then use ideas similar to those developed by Kashiwara and Vergne.
In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group G by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of G, viewed as continuous functions on the (possibly noncompact) Lie group G. In this talk, we will outline the main results of this paper and give additional conjectures.
Suppose HsubsetK are compact, connected Lie groups, and suppose tau is an irreducible, unitary representation of H. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of IndKHtau by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on K. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation pi of a reductive Lie group G when restricted to a reductive subgroup H. One of his key ideas was to restrict pi to a representation of a maximal compact subgroup KsubsetG, view pi as a subrepresentation of L2(K), and then use ideas similar to those developed by Kashiwara and Vergne.
In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group G by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of G, viewed as continuous functions on the (possibly noncompact) Lie group G. In this talk, we will outline the main results of this paper and give additional conjectures.
