Singular orbits of coadjoint action of Lie groups
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.
scientific article; zbMATH DE number 1281661