-
- SEKIGUCHI Hideko
- Department of Mathematics Kobe University
書誌事項
- タイトル別名
-
- The Penrose transform for Sp(n, \bm{R}) and singular unitary representations
この論文をさがす
抄録
We give a general definition of the Radon-Penrose transform for a Zuckerman-Vogan derived functor module of a reductive Lie group G, which maps from the Dolbeault cohomology group over a pseudo-Kähler homogeneous manifold into the space of smooth sections of a vector bundle over a Riemannian symmetric space. Furthermore, we formulate a functorial property between two Penrose trans-forms in the context of the Kobayashi theory of discretely decomposable restrictions of unitary representations.<br>Based on this general theory, we study the Penrose transform for a family of sin-gular unitary representations of Sp(n, \bm{R}) in details. We prove that the image of the Penrose transform is exactly the space of global holomorphic solutions of the system of partial differential equations of minor determinant type of odd degree over the bounded symmetric domain of type CI, which is biholomorphic to the Siegel upper half space. This system might be regarded as a generalization of the Gauss-Aomoto-Gelfand hy-pergeometric differential equations to higher order. We also find a new phenomenon that the kernel of the Penrose transform is non-zero, which we determine explicitly by means of representation theory.
収録刊行物
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 54 (1), 215-253, 2002
一般社団法人 日本数学会
- Tweet
キーワード
詳細情報 詳細情報について
-
- CRID
- 1390001205114560000
-
- NII論文ID
- 10007767590
-
- NII書誌ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- MRID
- 1864934
-
- NDL書誌ID
- 6080334
-
- 本文言語コード
- en
-
- データソース種別
-
- JaLC
- NDL
- Crossref
- CiNii Articles
-
- 抄録ライセンスフラグ
- 使用不可