Polynomial algebra associated to the Cartan subalgebra of G₂ in its enveloping algebra

Abstract The commutant of the Cartan subalgebra of G 2 in its enveloping algebra is determined, showing that it gives rise to a 66-dimensional polynomial algebra of sixth order. It is shown that the commutant of the regular subalgebra A 2 can be obtained by restriction. An illustration how to use these results for Hamiltonian systems with G 2 as spectrum generating algebra is given.