Existence of Weight Space Decompositions for Irreducible Representations of Simple Lie Algebras
- 1 January 1971
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 14 (1) , 113-115
- https://doi.org/10.4153/cmb-1971-021-7
Abstract
Let L denote a finite-dimensional simple Lie algebra over an algebraically closed field K of characteristic zero. It is well known that every finite-dimension 1, irreducible representation of L admits a weight space decomposition; moreover every irreducible representation of L having at least one weight space admits a weight space decomposition.Keywords
This publication has 3 references indexed in Scilit:
- Irreducible representations of a simple Lie algebra admitting a one-dimensional weight spaceProceedings of the American Mathematical Society, 1968
- Standard Representations of Simple Lie AlgebrasCanadian Journal of Mathematics, 1968
- On some applications of the universal enveloping algebra of a semisimple Lie algebraTransactions of the American Mathematical Society, 1951