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Lie Groups and Representation Theory
Seminar information archive ～03/19｜Next seminar｜Future seminars 03/20～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2023/06/13
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (The University of Tokyo)
Examples of discrete branching laws of derived functor modules (Japanese)
Yoshiki Oshima (The University of Tokyo)
Examples of discrete branching laws of derived functor modules (Japanese)
[ Abstract ]
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.
We consider the restriction of Zuckerman's derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable in the sense of Kobayashi. By using a classification result, it can be shown that the restriction decomposes as a direct sum of Zuckerman's derived functor modules for the subgroup. In the last talk, by using the realization of representations as D-modules, a decomposition of Zuckerman's modules corresponding to an orbit decomposition of flag varieties was explained. In this talk, we would like to see that such a decomposition can be written as a direct sum of Zuckerman's modules of the subgroup in some concrete examples.
