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- Title
On tensor induction of group representations.
- Authors
Kovács, L. G.
- Abstract
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.
- Publication
Journal of the Australian Mathematical Society, 1990, Vol 49, Issue 3, p486
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788700032456