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On tensor induction of group representations

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

L. G. Kovács
L. G. Kovács
Affiliation:
Mathematics IAS Australian National UniversityGPO Box 4 Canberra 2601, Australia
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Abstract

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Let G be a (not necessarily finite) group and ρ a finite dimensional faithful irreducible representation of G over an arbitrary field; write ρ¯ for ρ viewed as a projective representation. Suppose that ρ is not induced (from any proper subgroup) and that ρ¯ is not a tensor product (of projective representations of dimension greater than 1). Let K be a noncentral subgroup which centralizes all its conjugates in G except perhaps itself, write H for the normalizer of K in G, and suppose that some irreducible constituent, σ say, of the restriction p↓K is absolutely irreducible. It is proved that then (ρ is absolutely irreducible and) ρ¯ is tensor induced from a projective representation of H, namely from a tensor factor π of ρ¯↓H such that π↓K = σ¯ and ker π is the centralizer of K in G.

MSC classification

Secondary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 3 , December 1990 , pp. 486 - 501
Copyright
Copyright © Australian Mathematical Society 1990

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