Strongly orthogonal subsets in root systems (Q1599802)

A subset \(\Gamma\) of a finite root system \(\Delta\) is called strongly orthogonal (SOS) if when \(\alpha, \beta \in \Gamma\), \(\alpha \neq \beta\), then \(\alpha \pm \beta \not \in \Delta \cup \{0\}\). Such \(\Gamma\) occur in problems involving symmetric spaces. Two SOS of \(\Delta\) are equivalent if an element of the Weyl group of \(\Delta\) takes one to the other. The authors classify the maximal SOS (MSOS) and find the number of equivalences classes of MSOS. This number is \(1\) if \(\Delta=A_n\), \(B_n\) (\(n\) odd), \(D_n\), \(E_n\) or \(G_2\). It is \(2\) if \(\Delta=B_n\) (\(n\) even) or \(F_4\). It is \([n/2]+1\) if \(\Delta=C_n\) and is \(n+1\) if \(\Delta=BC_n\).