Geodesic
Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 583-592

Voir la notice de l'article provenant de la source Cambridge University Press

An element in the centre of the universal enveloping algebra of a semisimple Lie algebra was first constructed by Casimir by means of the Killing form. By Schur's lemma, in an irreducible finite-dimensional representation elements in the centre are represented by diagonal matrices of all whose eigenvalues are equal. In section 2 of this paper, we show the existence of a complete set of generators whose eigenvalues in an irreducible representation are closely related to polynomial invariants of the Weyl group W of the Lie algebra (Theorem 1). 
Lee, C. Y. Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 583-592. doi: 10.4153/CJM-1974-055-x
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