A Cohomology-Free Description of Eigencones in Types A, B, and C

Abstract

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