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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 $\tau_1, \dots, \tau_k$ of $G$ such that each $\tau_i$ is induced from a linear character of a subgroup of $G$ and such that $\sum^k_{i = 1} \tau_i = \sum_{\chi \in \text{Irr} (G)} \chi$. Models for the finite symmetric and general linear groups were described by Kljačko. Inglis, Richardson and Saxl have shown that there is a model $\tau_0, \tau_1, \dots, \tau_{[{n\over 2}]}$ for $S_n$, with $\tau_i$ 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.

20G05Representation theory of linear algebraic groups
20G40Linear algebraic groups over finite fields
Full Text: DOI
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