Irreducibility of tensor squares, symmetric squares and alternating squares

Kay Magaard, Gunter Malle, Pham Huu Tiep

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We investigate the question when the tensor square, the alternating square, or the symmetric square of an absolutely irreducible projective representation V of an almost simple group G is again irreducible. The knowledge of such representations is of importance in the description of the maximal subgroups of simple classical groups of Lie type. We show that if G is of Lie type in odd characteristic, either V is a Weil representation of a symplectic or unitary group, or G is one of a finite number of exceptions. For G in even characteristic, we derive upper bounds for the dimension of V which are close to the minimal possible dimension of nontrivial irreducible representations. Our results are complete in the case of complex representations. We will also answer a question of B. H. Gross about finite subgroups of complex Lie groups script G sign that act irreducibly on all fundamental representations of script G sign.

Original languageEnglish (US)
Pages (from-to)379-427
Number of pages49
JournalPacific Journal of Mathematics
Volume202
Issue number2
DOIs
StatePublished - Jan 1 2002

ASJC Scopus subject areas

  • Mathematics(all)

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