The Penrose Transform for Certain Non-Compact Homogeneous Manifolds of $U(n,n)$

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概要

• 論文の詳細を見る

• We construct \lq\lq{the Penrose transform}\rq\rq\ as an intertwining operator between two different geometric realization of infinite dimensional representations of $U(n,n)$, namely, from the space of the Dolbeault cohomology group on a non-compact complex homogeneous manifold to the space of holomorphic functions over the bounded domain of type $AIII$. We show that the image of the Penrose transform satisfies the system $(\Cal M_k)$ of partial differential equations of order $k+1$ which we find in explicit forms. Conversely, we also prove that any solution of the system $(\Cal M_k)$ is uniquely obtained as the image of the Penrose transform, by using the theory of prehomogeneous vector spaces.

• 東京大学の論文
• 1996-00-00

著者

• Sekiguchi Hideko

  Department Of Mathematical Sciences University Of Tokyo

• Sekiguchi Hideko

  Department of Mathematics, Kobe University

関連論文

• Commuting families of differential operators invariant under the action of a Weyl group
• Combinatorial formula of the dimension of global solutions to a generalized hypergeometric system Μ_(ν)
• The Penrose transform for Sp(n, R) and singular unitary representations
• The Penrose Transform for Certain Non-Compact Homogeneous Manifolds of $U(n,n)$

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