Article

Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 91, Issue 3, pp 167-182

On invariant convex cones in simple Lie algebras

  • S. KumaresanAffiliated withSchool of Mathematics, Tata Institute of Fundamental Research
  • , Akhil RanjanAffiliated withSchool of Mathematics, Tata Institute of Fundamental Research

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Abstract

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.

Keywords

Lie algebra adjoint group invariant convex cones