Coadjoint Orbits of Siegel Parabolic Subgroups
نویسنده
چکیده
Let P+(n) be the Siegel parabolic subgroup of O(n, n), and P−(n) be the Siegel parabolic subgroup of Sp2n(R). In this paper, we study the coadjoint orbits of P±(n). We establish a one-to-one correspondence between the real coadjoint orbits of Sp2n(R) and the principal coadjoint orbits of P+(2n), and a one-to-one correspondence between the real coadjoint orbits of O(p, n− p) with p ∈ [0, n] and the principal real coadjoint orbits of P−(n).
منابع مشابه
Regular Orbits of Symmetric Subgroups on Partial Flag Varieties
The main result of the current paper is a new parametrization of the orbits of a symmetric subgroup K on a partial flag variety P . The parametrization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the other. One of our motivations, as explained below, is related to enumerating special unipotent representations of real reductive groups. Another mot...
متن کاملCoadjoint Orbits of the Virasoro Group
The coadjoint orbits of the Virasoro group, which have been investigated by Lazutkin and Pankratova and by Segal, should according to the Kirillov-Kostant theory be related to the unitary representations of the Virasoro group. In this paper, the classification of orbits is reconsidered, with an explicit description of the possible centralizers of coadjoint orbits. The possible orbits are diff(S...
متن کاملThe Orbit Method for the Jacobi Group
g∗ −→ g, λ 7→ Xλ characterized by λ(Y ) =< Xλ, Y >, Y ∈ g. Therefore the coadjoint G-orbits in g∗ may be identified with adjoint G-orbits in g. The philosophy of the orbit method says that we may attach the irreducible unitary representations of G to the coadjoint orbits in g∗. Historically the orbit method that was first initiated by A.A. Kirillov (cf. [K]) early in the 1960s in a real nilpote...
متن کاملLine Bundles on Spectral Curves and the Generalised Legendre Transform Construction of Hyperkähler Metrics
An analogue of the correspondence betweenGL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K ⊂ GL(k) is one of the following: maximal parabolic, maximal torus, GL(k − 1) embedded diagonally. The generalised Legendre transform construction of hyperkähler metrics is studied further, showing that many known hyperkähler metrics (including the ...
متن کاملLine Bundles on Spectral Curves and the Generalised Legendre Transform
An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K ⊂ GL(k) is one of the following: maximal parabolic, maximal torus, GL(k − 1) embedded diagonally. The generalised Legendre transform construction of hyperkähler metrics is studied further, showing that many known hyperkähler metrics (including the...
متن کامل