Distinguished orbits of reductive groups

Distinguished Orbits of Reductive Groups

We prove a generalization and give a new proof of a theorem of Borel-Harish-Chandra on closed orbits of linear actions of reductive groups. Consider a real reductive algebraic group G acting linearly and rationally on a real vector space V . G can be viewed as the real points of a complex reductive group G C which acts on V C := V ⊗ C. In [BHC62] it was shown that G · v ∩ V is a finite union of...

ADMISSIBLE NILPOTENT COADJOINT ORBITS OF p-ADIC REDUCTIVE LIE GROUPS

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...

The method of coadjoint orbits for real reductive groups

Distinguished Orbits and the L-s Category of Simply Connected Compact Lie Groups

We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group on the Lie algebra of a maximal torus of G.

Reductive Groups