Let f : Ω→Gr(n,H) be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr(n,H) the Grassmannian manifold. Denote by Ef the "pull back" bundle induced by f. We ...Let f : Ω→Gr(n,H) be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr(n,H) the Grassmannian manifold. Denote by Ef the "pull back" bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn(Ω). Moreover, we compute the maximal self-adjoint subalgebra of A'(Ef) and A'(T) respectively. Finally, we fix the masa of A'(Ef) and .A' (T) which depends on the HIR decomposition of Ef or T respectively.展开更多
文摘Let f : Ω→Gr(n,H) be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr(n,H) the Grassmannian manifold. Denote by Ef the "pull back" bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn(Ω). Moreover, we compute the maximal self-adjoint subalgebra of A'(Ef) and A'(T) respectively. Finally, we fix the masa of A'(Ef) and .A' (T) which depends on the HIR decomposition of Ef or T respectively.