Fix a Cartan subalgebra $\mathfrak{h}$ on a (compact simple) Lie algebra $\mathfrak{g}$ and consider the associated root system. If $\alpha$ is a root, it is well-known that $k\alpha$ is also a root if and only if $k=\pm1$.
Is there any similar statement for (compact, irreducible) symmetric spaces?
Actually my main interest is that 3/2 does not appear as a multiple of a root in $SU(2n)/Sp(n)$ (or 9/4 as a multiple of a real root), but I am still incapable of reading Dynkin/Satake/Vogan-diagrams.
Thanks in advance.