On invariant convex cones in simple Lie algebras
- 27 Downloads
This paper is devoted to a study and classification ofG-invariant convex cones ing, whereG is a lie group andg its Lie algebra which is simple. It is proved that any such cone is characterized by its intersection withh-a fixed compact Cartan subalgebra which exists by the very virtue of existence of properG-invariant cones. In fact the pair (g,k) is necessarily Hermitian symmetric.
KeywordsLie algebra adjoint group invariant convex cones
- Duistermaat J J, Kolk J A C and Varadarajan V S 1981 Preprint No. 200, University UtrechtGoogle Scholar
- Heckman G J 1980 Projection of orbits and asymptotic behaviour of multiplicities for compact Lie groups. Thesis Rijksuniversiteit LeidenGoogle Scholar
- Warner G 1972Harmonic analysis on semisimple Lie groups Vol. I (Berlin: Springer Verlag)Google Scholar