I will introduce root systems, which are nice combinatorial objects, coming with a height function with values in Z, and will consider the question, raised in a recent preprint by Dipendra Prasad and al., to determine the subsystem of roots whose height is a multiple of a fixed integer m. I will illustrate this for the series \(A_n\) and \(B_n\). Time permitting, I will mention Weyl\'s dimension formula and explain the context of the question by D. Prasad and al.
