Invariant Polynomials of Weyl Groups and Applications to the Centres of Universal Enveloping Algebras
1974 ◽
Vol 26
(3)
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pp. 583-592
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Keyword(s):
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).
2013 ◽
Vol 12
(05)
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pp. 1250207
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1966 ◽
Vol 27
(2)
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pp. 531-542
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2002 ◽
Vol 15
(5)
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pp. 527-532
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2014 ◽
Vol 150
(9)
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pp. 1579-1606
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2001 ◽
Vol 16
(29)
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pp. 4769-4801
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1993 ◽
Vol 08
(20)
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pp. 3479-3493
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