### Abstract

Let G be a finite simple group of Lie type, and let π_{G} 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 π_{G}, unless G=PSU_{n}(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 language | English (US) |
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Pages (from-to) | 908-930 |

Number of pages | 23 |

Journal | Proceedings of the London Mathematical Society |

Volume | 106 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2013 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Heide, G., Saxl, J., Tiep, P. H., & Zalesski, A. E. (2013). Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type.

*Proceedings of the London Mathematical Society*,*106*(4), 908-930. https://doi.org/10.1112/plms/pds062