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Lie群論・表現論セミナー
過去の記録 ～05/23｜次回の予定｜今後の予定 05/24～
| 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 |
2017年09月26日(火)
17:00-18:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同
関口英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (Japanese)
トポロジー火曜セミナーと合同
関口英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (Japanese)
[ 講演概要 ]
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces X of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when X is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive k-planes in Cp,q (1≤k≤min) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive k-planes and that of negative k-planes.
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces X of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when X is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive k-planes in Cp,q (1≤k≤min) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive k-planes and that of negative k-planes.
