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Proof of Verma’s conjecture on Weyl’s dimension polynomial. (English) Zbl 0298.17005

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
17B45 Lie algebras of linear algebraic groups
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References:
[1] Bourbaki, N.: Groupes et algèbres de Lie, Chap. IV-VI. Paris: Hermann 1969
[2] Steinberg, R.: Differential equations invariant under finite reflection groups. Trans. AMS112, 392-400 (1964) · Zbl 0196.39202
[3] Verma, D.-N.: Rôle of affine Weyl groups in the representation theory of algebraic Chevalley groups and their Lie algebras, (preprint, 1972) to appear in ?Lie groups and their representations? Proceedings of the 1971 Summer School on Representation Theory (Ed.: I.M. Gel’fand). Budapest: Akadémiai Kiadó
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