Classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits
| dc.creator | Tumpach, Alice Barbara | |
| dc.date | 2007-03-13 | |
| dc.date.accessioned | 2026-07-07T07:51:39Z | |
| dc.date.available | 2026-07-07T07:51:39Z | |
| dc.description | 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 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 (g, k), where g is a simple L*-algebra and k a subalgebra of g, to construct an increasing sequence of finite-dimensional subalgebras g_n of g together with an increasing sequence of finite-dimensional subalgebras k_n of k such that g (resp. k) is the closure of the union of g_n (resp. k_n), and such that the pairs (g_n, k_n) are symmetric. Comparing with the classification of Hermitian-symmetric spaces given by W. Kaup, it follows that any Hermitian-symmetric space of compact type is an affine-coadjoint orbit of an Hilbert Lie group. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0703042 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0703042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125593 | |
| dc.subject | Mathematical Physics | |
| dc.title | Classification of infinite-dimensional irreducible Hermitian-symmetric affine coadjoint orbits | |
| dc.type | text |