Borel-Weil Theory for Root Graded Banach-Lie groups
| dc.creator | Mueller, Christoph | |
| dc.creator | Neeb, Karl-Hermann | |
| dc.creator | Seppanen, Henrik | |
| dc.date | 2009-03-06 | |
| dc.date.accessioned | 2026-07-07T12:49:52Z | |
| dc.date.available | 2026-07-07T12:49:52Z | |
| dc.description | In this paper we introduce (weakly) root graded Banach--Lie algebras and corresponding Lie groups as natural generalizations of group like $\GL_n(A)$ for a Banach algebra $A$ or groups like $C(X,K)$ of continuous maps of a compact space $X$ into a complex semisimple Lie group $K$. We study holomorphic induction from holomorphic Banach representations of so-called parabolic subgroups $P$ to representations of $G$ on holomorphic sections of homogeneous vector bundles over $G/P$. One of our main results is an algebraic characterization of the space of sections which is used to show that this space actually carries a natural Banach structure, a result generalizing the finite dimensionality of spaces of sections of holomorphic bundles over compact complex manifolds. We also give a geometric realization of any irreducible holomorphic representation of a (weakly) root graded Banach--Lie group $G$ and show that all holomorphic functions on the spaces $G/P$ are constant. | |
| dc.identifier | https://arxiv.org/abs/0903.1188 | |
| dc.identifier | http://arxiv.org/abs/0903.1188 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222517 | |
| dc.subject | Representation Theory | |
| dc.subject | Complex Variables | |
| dc.title | Borel-Weil Theory for Root Graded Banach-Lie groups | |
| dc.type | text |