Complexity of nilpotent orbits and the Kostant-Sekiguchi correspondence
Representation Theory
2007-05-23 v1 Symplectic Geometry
Abstract
Let G be a connected linear semisimple Lie group with Lie algebra g, and let K_C --> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space G/K. Suppose that O is a nilpotent G-orbit in g and O* is the nilpotent K_C-orbit in p_C associated to O by the Kostant-Sekiguchi correspondence. We show that the complexity of O* as a K_C variety measures the failure of the Poisson algebra of smooth K-invariant functions on O to be commutative.
Keywords
Cite
@article{arxiv.math/0303096,
title = {Complexity of nilpotent orbits and the Kostant-Sekiguchi correspondence},
author = {Donald R. King},
journal= {arXiv preprint arXiv:math/0303096},
year = {2007}
}
Comments
7 pages