Lie群論・表現論セミナー

過去の記録 ~03/28次回の予定今後の予定 03/29~

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)
[ 講演概要 ]
Suppose $H\\subset K$ 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 $Ind_H^K\\tau$ 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 $K\\subset G$, view $\\pi$ as a subrepresentation of $L^2(K)$, 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.