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Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras

Published online by Cambridge University Press:  20 November 2018

C. Y. Lee
C. Y. Lee*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 583 - 592
Copyright
Copyright © Canadian Mathematical Society 1974

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