Article contents
Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras
Published online by Cambridge University Press: 20 November 2018
Extract
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
- Copyright
- Copyright © Canadian Mathematical Society 1974
References
- 7
- Cited by