トポロジー火曜セミナー

過去の記録 ~09/19次回の予定今後の予定 09/20~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://faculty.ms.u-tokyo.ac.jp/~topology/index.html
備考 Tea: 16:30 - 17:00 コモンルーム

2017年09月26日(火)

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00, Lie群論・表現論セミナーと合同
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 ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) 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.