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Zbl 0826.20038
Inglis, N.F.J.; Saxl, J.
An explicit model for the complex representations of the finite general linear groups.
(English)
[J] Arch. Math. 57, No.5, 424-431 (1991). ISSN 0003-889X; ISSN 1420-8938/e

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.
MSC 2000:
*20G05 Representation theory of linear algebraic groups
20G40 Linear algebraic groups over finite fields

Keywords: complex representations; linear characters of subgroups; irreducible characters; general linear groups

Cited in: Zbl 1250.22016 Zbl 1011.20014

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