In this paper we obtain an algebraic classification of all homogeneous Hermitian holomorphic vector bundles of arbitrary rank over a bounded symmetric domain. This classification result is used in order to classify, up to unitary equivalence, all irreducible homogeneous bounded linear operators on a separable infinite-dimensional Hilbert space that belong to the Cowen-Douglas class B2 (∆), where ∆ is the open unit disk.
SynopsisWe consider the Yang–Mills functional denned on connections on a principal bundle over a compact Riemannian manifold of dimension 2 or 3. It is shown that if we consider the Yang–Mills functional as being defined on an appropriate Hilbert manifold of orbits of connections under the action of the group of principal bundle automorphisms, then the functional satisfies the Palais–Smale condition.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.