2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66729Let 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.7 pagesRepresentation TheorySymplectic Geometry22E46(primary), 14R20(secondary), 53D20(secondary)text