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Lie Groups and Representation Theory
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2007/05/17
15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
真野元 (東京大学数理科学研究科)
The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
真野元 (東京大学数理科学研究科)
The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)
[ Abstract ]
The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.
This is a joint work with T. Kobayashi.
[ Reference URL ]The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.
This is a joint work with T. Kobayashi.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
