On the classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
-
Alice Barbara Tumpach
Abstract
In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type, which is a particular example of an Hilbert manifold, is transitively acted upon by a Hilbert Lie group of isometries. In this paper we give the classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits of connected simple L*-groups of compact type using the notion of simple roots of non-compact type. The key step is, given an infinite-dimensional symmetric pair (
, 
), where is a simple L*-algebra of compact type and a subalgebra of , to construct an increasing sequence of finite-dimensional subalgebras n of together with an increasing sequence of finite-dimensional subalgebras n of such that 
, 
, and such that the pairs (n, n) are symmetric. Comparing with the classification of Hermitian-symmetric spaces given by W. Kaup, it follows that any Hermitian-symmetric space of compact or non-compact type is an affine-coadjoint orbit of an Hilbert Lie group.
© de Gruyter 2009
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Artikel in diesem Heft
- On the classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
- A partial generalization of the Helgason Conjecture to general bounded homogeneous domains
- Antisymmetric elements in group rings with an orientation morphism
- Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem
- On loops rich in automorphisms that are abelian modulo the nucleus
- Minimal number of periodic points for C1 self-maps of compact simply-connected manifolds
- On a question of Bombieri and Bourgain
- Separate real analyticity and CR extendibility
- Coverings of Banach spaces: beyond the Corson theorem
- Genus 2 curves that admit a degree 5 map to an elliptic curve
