Representations of generic algebras and finite groups of Lie type

Howlett, R. B.; Lehrer, G. I.

doi:10.1090/S0002-9947-1983-0716849-6

Representations of generic algebras and finite groups of Lie type
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by R. B. Howlett and G. I. Lehrer

Trans. Amer. Math. Soc. 280 (1983), 753-779

DOI: https://doi.org/10.1090/S0002-9947-1983-0716849-6

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Abstract:

The complex representation theory of a finite Lie group $G$ is related to that of certain "generic algebras". As a consequence, formulae are derived ("the Comparison Theorem"), relating multiplicities in $G$ to multiplicities in the Weyl group $W$ of $G$. Applications include an explicit description of the dual (see below) of an arbitrary irreducible complex representation of $G$.

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