Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]