J Austral Math Soc Ser A 49 pp486--501, 1990.

On Tensor Induction of Group Representations

L. G. Kovács

Abstract

Let G be a (not necessarily finite) group r a finite dimensional faithful irreducible representation of G over an arbitrary field; write¾r for r viewed as a projective representation. Suppose that r is not induced (from any proper subgroup) and that¾r 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, s say, of the restriction r¯_K is absolutely irreducible. It is proved that then (r is absolutely irreducible)¾r is tensor induced from a projective representation of H, namely from a tensor factor p of¾r¯_H such that p¯_K = ¾s and kerp is the centralizer of K in G.

1980 AMS Subject Classification (1985 Revision): primary 20C15, 20C20

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Authors

L. G. Kovács

Mathematics IAS, Australian National University, GPO Box 4, Canberra 2601, Australia.