A new matrix method for the Casimir operators of the Lie algebras wsp (N,R) and Isp (2N,R)

Abstract

A method is given to determine the Casimir operators of the perfect Lie algebras wsp (N,R) = sp (2N,R)−→⊕Γω1 ⊕Γ0hN and the inhomogeneous Lie algebrasIsp (2N,R) in terms of polynomials associated to a parametrized (2N + 1)×(2N + 1)-matrix. For the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation. The method is extended to other classes of Lie algebras, and some applications to the missing label problem are given.