A cohomology free description of eigencones in type A, B and C

Abstract

Let $K$ be a connected compact Lie group. The triples $(O_1,\,O_2,\,O_3)$ of adjoint $K$-orbits such that $O_1+O_2+O_3$ contains $0$ are parametrized by a closed convex polyhedral cone called the eigencone of $K$. For $K$ simple of type $A$, $B$ or $C$ we give an inductive cohomology free description of the minimal set of linear inequalities which characterizes the eigencone of $K$.