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Lie Groups and Representation Theory
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2022/04/26
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology
Yoshiki Oshima (The University of Tokyo)
On the existence of discrete series for homogeneous spaces (Japanese)
Joint with Tuesday Seminar on Topology
Yoshiki Oshima (The University of Tokyo)
On the existence of discrete series for homogeneous spaces (Japanese)
[ Abstract ]
When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to
see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.
When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to
see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.
