Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type

Gerhard Heide, Jan Saxl, Pham Huu Tiep, Alexandre E. Zalesski

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Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n≥3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.

Original languageEnglish (US)
Pages (from-to)908-930
Number of pages23
JournalProceedings of the London Mathematical Society
Issue number4
StatePublished - Apr 1 2013


ASJC Scopus subject areas

  • Mathematics(all)

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