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An explicit model for the complex representations of the finite general linear groups. (English) Zbl 0826.20038
A model for the complex representations of a finite group G is a set of characters τ 1 ,,τ k of G such that each τ i is induced from a linear character of a subgroup of G and such that i=1 k τ i = χIrr(G) χ. Models for the finite symmetric and general linear groups were described by Kljačko. Inglis, Richardson and Saxl have shown that there is a model τ 0 ,τ 1 ,,τ [n 2] for S n , with τ i a sum of all irreducible characters of S n corresponding to partitions with precisely n-2i odd parts. In this paper we show that a suitable analogy holds for a model of the general linear groups.

MSC:
20G05Representation theory of linear algebraic groups
20G40Linear algebraic groups over finite fields
References:
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