Share

# Unitary representations of maximal parabolic subgroups of the classical groups

• ·

Written in English

### Subjects:

• Lie groups.,
• Representations of groups.,
• Linear algebraic groups.

## Book details:

Edition Notes

Classifications The Physical Object Statement Joseph A. Wolf. Series Memoirs of the American Mathematical Society ; no. 180, Memoirs of the American Mathematical Society ;, no. 180. LC Classifications QA3 .A57 no. 180, QA387 .A57 no. 180 Pagination iii, 193 p. ; Number of Pages 193 Open Library OL4900331M ISBN 10 0821821806 LC Control Number 76044397

### Download Unitary representations of maximal parabolic subgroups of the classical groups

PDF EPUB FB2 MOBI RTF

Part II: Unitary Groups 24 30 §2. Parabolic Subgroups of Unitary Groups: Statement of Structure 24 30 §3. Parabolic Subgroups of Unitary Groups: Proof of Structure 31 37 §4. Unitary Representations of the Nilradical 41 47 §5. Representations of the Groups G[sub(s;t,u)](F) 48 54 §6. Representations of the Maximal Parabolic Subgroups 60 66 §7. In this paper, we study the restriction of an irreducible unitary representation $\pi$ of the universal covering $\widetilde{Sp}_{2n}(\mb R)$ to a Heisenberg maximal parabolic group $\tilde P$.Author: Hongyu He. 8, of subgroups of the ﬁnite classical groups and proves that a maximal subgroup either belongs to one of these classes or has a non–abelian simple group as its generalized Fitting subgroup. In their book [12], P.B. Kleidman and M.W. Liebeck have identiﬁed the members of the eight classes for modules with dimension greater t 1. In this paper we prove the unitarity of duals of tempered representations supported on minimal parabolic subgroups for split classical p-adic groups.

This is the symplectic group of the form B. The goal is to work out the structure of what are called maximal parabolic sub-groups of Sp(V), and to look at the corresponding geometry. De nition 2. An isotropic subspace of V is a vector subspace S ˆ V with the property that B(v;w) = 0 (v;w 2 S). Cite this paper as: Wolf J.A. () Representations that remain irreducible on parabolic subgroups. In: García P.L., Pérez-Rendón A., Souriau J.M. (eds) Differential Geometrical Methods in . Download Normalizers Of Parabolic Subgroups In Unitary Reflection Groups full book in PDF, EPUB, and Mobi Format, get it for read on your Kindle device, PC, phones or tablets. Normalizers Of Parabolic Subgroups In Unitary Reflection Groups full free pdf books. 1. Simple constructions of irreducible unitary representations In this paper we shall deal with representations of (connected) classical complex groups. For such a group G we shall ﬁx a maximal compact subgroup K of G. The complexiﬁed Lie algebra of G, viewed as a real Lie group.

Unitary representations of maximal parabolic subgroups of the classical groups. Memoirs of the American Mathematical Society, Number , See the AMS web page here; Conformal group, quantization, and the Kepler problem. The Theory of Unitary Group Representations | Mackey, G.W. | download | B–OK. Download books for free. Find books Unitary Representations of Maximal Parabolic Subgroups of the Classical Groups. Amer Mathematical Society. J. Wolf. Year: Whether you've loved the book or not, if you give your honest and detailed thoughts then. transitively on G/K, the group N has square integrable representations [15]. And it is known just which maximal parabolic subgroups of semisimple Lie groups have square integrable nilradical [14]. In [17] and [18] the theory of square integrable nilpotent groups was extended to “stepwise square integrable” nilpotent groups. We study the structure of minimal parabolic subgroups of the classical infinite-dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of parabolic subgroups and subalgebras that are not necessarily direct limits of finite-dimensional parabolics.