Geodesic
One-Dimensional Representations of the Cycle Subalgebra of a Semi-Simple Lie Algebra
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 463-467

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Let L denote a semi-simple, finite dimensional Lie algebra over an algebraically closed field K of characteristic zero. If denotes a Cartan subalgebra of L and denotes the centralizer of in the universal enveloping algebra U of L, then it has been shown that each algebra homomorphism (called a "mass-function" on ) uniquely determines a linear irreducible representation of L. The technique involved in this construction is analogous to the Harish-Chandra construction [2] of dominated irreducible representations of L starting from a linear functional . The difference between the two results lies in the fact that all linear functionals on are readily obtained, whereas since is in general a noncommutative algebra the construction of mass-functions is decidedly nontrivial. 
Lemire, F. W. One-Dimensional Representations of the Cycle Subalgebra of a Semi-Simple Lie Algebra. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 463-467. doi: 10.4153/CMB-1970-085-9
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     author = {Lemire, F. W.},
     title = {One-Dimensional {Representations} of the {Cycle} {Subalgebra} of a {Semi-Simple} {Lie} {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {463--467},
     year = {1970},
     volume = {13},
     number = {4},
     doi = {10.4153/CMB-1970-085-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-085-9/}
}
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