Complete reducibility and separability

@article{Bate2007CompleteRA,
  title={Complete reducibility and separability},
  author={Michael Bate and Benjamin Martin and Gerhard R{\"o}hrle and Rudolf Tange},
  journal={Transactions of the American Mathematical Society},
  year={2007},
  volume={362},
  pages={4283-4311}
}
  • M. BateB. Martin R. Tange
  • Published 24 September 2007
  • Mathematics
  • Transactions of the American Mathematical Society
Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the interaction between the notion of separability and Serre's concept of G-complete reducibility for subgroups of G. The separability hypothesis appears in many general theorems concerning G-complete reducibility. We demonstrate that many of these results fail without… 

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