Rutwig Campoamor-Stursberg
A new matrix method for the Casimir operators of the Lie algebras 
$w\frak{sp}\left( N,\mathbb{R}\right) $ and $I\frak{sp}\left( 
2N,\mathbb{R}\right) $.
(254K, PDF)

ABSTRACT.  A method is given to determine the Casimir operators of the perfect Lie 
algebras $w\frak{sp}\left( N,\mathbb{R}\right) =\frak{sp}\left( 
2N,\mathbb{R}\right) \overrightarrow{\oplus}_{\Gamma_{\omega_{1}}\oplus 
\Gamma_{0}}\frak{h}_{N}$ and the inhomogeneous Lie algebras 
$I\frak{sp}\left( 2N,\mathbb{R}\right) $ in terms of polynomials associated to a parametrized $\left(2N+1\right)\times\left( 2N+1\right) $-matrix. For the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation.\newline The method is extended to other classes of Lie algebras, and some applications to the missing label problem are given.