Abstract

We consider a family of singular infinite dimensional unitary representations of G = Sp(n, ℝ) which are realized as sheaf cohomology spaces on an open G-orbit D in a generalized flag variety for the complexification of G. By parametrizing an appropriate space, M_D, of maximal compact subvarieties in D, we identify a holomorphic double fibration between D and M_D which we use to define a map P, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on M_D. Analysis of the construction of P shows that P is injective, the image of P is the kernel of a differential operator on M_D and P is an intertwining map.

We consider a family of singular infinite dimensional unitary representations of G = Sp(n, ℝ) which are realized as sheaf cohomology spaces on an open G-orbit D in a generalized flag variety for the complexification of G. By parametrizing an appropriate space, M_D, of maximal compact subvarieties in D, we identify a holomorphic double fibration between D and M_D which we use to define a map P, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on M_D. Analysis of the construction of P shows that P is injective, the image of P is the kernel of a differential operator on M_D and P is an intertwining map.

We consider a family of singular infinite dimensional unitary representations of $G=Sp\left(n,ℝ\right)$ which are realized as sheaf cohomology spaces on an open $G$-orbit $D$ in a generalized flag variety for the complexification of $G$. By parametrizing an appropriate space, $M_D$, of maximal compact subvarieties in $D$, we identify a holomorphic double fibration between $D$ and $M_D$ which we use to define a map $P$, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on $M_D$. Analysis of the construction of $P$ shows that $P$ is injective, the image of $P$ is the kernel of a differential operator on $M_D$ and $P$ is an intertwining map.

We consider a family of singular infinite dimensional unitary representations of $G=Sp\left(n,ℝ\right)$ which are realized as sheaf cohomology spaces on an open $G$-orbit $D$ in a generalized flag variety for the complexification of $G$. By parametrizing an appropriate space, $M_D$, of maximal compact subvarieties in $D$, we identify a holomorphic double fibration between $D$ and $M_D$ which we use to define a map $P$, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on $M_D$. Analysis of the construction of $P$ shows that $P$ is injective, the image of $P$ is the kernel of a differential operator on $M_D$ and $P$ is an intertwining map.

We consider a family of singular infinite dimensional unitary representations of G = Sp(n, R) which are realized as sheaf cohomology spaces on an open G-orbit D in a generalized flag variety for the complexification of G. By parametrizing an appropriate space, M_D, of maximal compact subvarieties in D, we identify a holomorphic double fibration between D and M_D which we use to define a map P, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on M_D. Analysis of the construction of P shows that P is injective, the image of P is the kernel of a differential operator on M_D and P is an intertwining map.

Authors