Coxeter element and particle masses
Let $${\mathfrak {g}}$$g be a simple Lie algebra of rank r over $$\mathbb {C}, {\mathfrak {h}}\subset {\mathfrak {g}}$$C,h⊂g a Cartan subalgebra. We construct a family of r commuting Hermitian operators acting on $${\mathfrak {h}}$$h whose eigenvalues are equal to the coordinates of the eigenvectors of the Cartan matrix of $${\mathfrak {g}}$$g.