### Abstract

To Burkhard Külshammer on his sixtieth birthday

Original language | English |
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Pages (from-to) | 463-470 |

Number of pages | 8 |

Journal | Israel Journal of Mathematics |

Volume | 214 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jul 2016 |

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### Cite this

*Israel Journal of Mathematics*,

*214*(1), 463-470. https://doi.org/10.1007/s11856-016-1337-2

**On a question of Külshammer for representations of finite groups in reductive groups.** / Bate, Michael; Martin, Benjamin; Rohrle, Gerhard.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 214, no. 1, pp. 463-470. https://doi.org/10.1007/s11856-016-1337-2

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TY - JOUR

T1 - On a question of Külshammer for representations of finite groups in reductive groups

AU - Bate, Michael

AU - Martin, Benjamin

AU - Rohrle, Gerhard

N1 - Acknowledgments. The authors acknowledge the financial support of EPSRC Grant EP/L005328/1, Marsden Grants UOC1009 and UOA1021, and the DFG-priority programme SPP1388 “Representation Theory”. We are grateful to the referee for helpful suggestions.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Let G be a simple algebraic group of type G2 over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ2 and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ2 are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre.To Burkhard Külshammer on his sixtieth birthday

AB - Let G be a simple algebraic group of type G2 over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ2 and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ2 are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre.To Burkhard Külshammer on his sixtieth birthday

U2 - 10.1007/s11856-016-1337-2

DO - 10.1007/s11856-016-1337-2

M3 - Article

VL - 214

SP - 463

EP - 470

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -