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2139-02.pdf | 8.09 MB | Adobe PDF | 見る/開く |
タイトル: | A generalized uniformly bounded multiplicity theorem (Developments in Representation Theory and Related Topics) |
著者: | 田内, 大渡 ![]() |
著者名の別形: | Tauchi, Taito |
発行日: | Dec-2019 |
出版者: | 京都大学数理解析研究所 |
誌名: | 数理解析研究所講究録 |
巻: | 2139 |
開始ページ: | 11 |
終了ページ: | 28 |
抄録: | Let P be a minimal parabolic subgroup of a real reductive Lie group G and H a closed subgroup of G. Then it is proved by T. Kobayashi and T. Oshima that the regular representation C∞ (G/H) contains each irreducible representation of G at most finitely many times if the number of H-orbits on G/P is finite. Moreover, they also proved that the multiplicities are uniformly bounded if the number of He-orbits on Gc/B is finite, where Gc, He are complexifications of G, H, respectively, and B is a Borel subgroup of Ge. In this paper, we prove that the multiplicities of the representations of G induced from a parabolic subgroup Q in the regular representation on G/H are uniformly bounded if the number of Heorbits on Gc/Qc is finite. For the proof of this claim, we also prove the uniform boundedness of the dimensions of the spaces of group invariant hyperfunctions using the theory of holonomic Dx-modules. |
URI: | http://hdl.handle.net/2433/254903 |
出現コレクション: | 2139 表現論とその周辺分野の進展 |
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