04-381 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) Nov 13, 04

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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.

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