✦ LIBER ✦

On finite degree partial representations of groups

✍ Scribed by M. Dokuchaev; N. Zhukavets

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 304 KB
Volume: 274
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00533-7

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✦ Synopsis

We establish a one-to-one correspondence between the irreducible finite degree partial representations of a group G and the (usual) irreducible representations of certain ideals of a groupoid algebra constructed from G. We derive a structural result about the irreducible partial representations on finite dimensional vector spaces and give the description "up to usual representations" of the irreducible partial representations of abelian groups of degrees 4. We treat simultaneously irreducible and indecomposable partial representations.

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This paper studies finite linear groups of relatively small degree over I~, the real numbers, and Q, the rationals. Throughout the paper, G denotes a finite group, p a fixed rational prime which divides IG[, P a Sylow p-subgroup of G, and 1 ~ the trivial character for G over a field of characteristi