Irreducibility of tensor squares, symmetric squares and alternating squares

Kay Magaard, Gunter Malle, Pham Huu Tiep

Research output: Contribution to journalArticle

22 Citations (Scopus)

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
StatePublished - 2002
Externally publishedYes

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Irreducibility
Tensor
Simple group
Weil Representation
Projective Representation
Groups of Lie Type
Symplectic Group
Maximal Subgroup
Classical Groups
Unitary group
Gross
Irreducible Representation
Exception
Odd
Subgroup
Upper bound

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Irreducibility of tensor squares, symmetric squares and alternating squares. / Magaard, Kay; Malle, Gunter; Tiep, Pham Huu.

In: Pacific Journal of Mathematics, Vol. 202, No. 2, 2002, p. 379-427.

Research output: Contribution to journalArticle

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