Singular orbits of coadjoint action of Lie groups
type: Item
instance of: scholarly article
title: Singular orbits of coadjoint action of Lie groups
zbMATH Open document ID: 0914.22010
published in: Regular and Chaotic Dynamics
publication date: 1999-06-14T00:00:00Z
review text: Let \(G\) be \(SO(n)\) or \(E(n)\), the Euclidean group. This paper realizes some of the singular coadjoint orbits of \(G\) as level surfaces of certain polynomials (usually Pfaffians or coefficients of a characteristic polynomial). The particular orbits realized are \(SO(2n)/SO(2k)\times SO(2)^{n-k}\), \(SO(2n+1)/SO(2k+1)\times SO(2)^{n-k}\), \(E(2n)/{\mathbb R}\times SO(2k+1)\times SO(2)^{n-k-1}\), and \(U(n)/U(2k)\times U(2)^{n-k}\). These orbits include the minimal dimensional ones and turn out to be given by the intersection of quadrics.
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 1281661
zbMATH Keywords: Euclidean group
zbMATH Keywords: singular coadjoint orbits
zbMATH Keywords: Pfaffians
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: quadrics
author: A. Boyarsky
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
DOI: 10.1070/RD1998V003N02ABEH000074
description: scientific article; zbMATH DE number 1281661