Strongly orthogonal subsets in root systems

Abstract

We classify maximal strongly orthogonal subsets ( =MSOS 's) in irreducible root systems under the action of Weyl groups, including non-reduced cases. We show that among irreducible root systems, B_{n}(n=even) , C_{n}(n\geq 2) , F_{4} and BC_{n}(n\geq 1) admit several inequivalent MSOS's. As an application of this result, we give a classification of MSOS 's associated with Riemannian symmetric pairs.