Corpus ID: 119307507

An algorithmic approach to perverse derived equivalences: Brou\'e's Conjecture for $\Omega^{+}_8(2)$

@article{Sannella2018AnAA,
  title={An algorithmic approach to perverse derived equivalences: Brou\'e's Conjecture for \$\Omega^\{+\}_8(2)\$},
  author={Stefano Sannella},
  journal={arXiv: Representation Theory},
  year={2018}
}
  • Stefano Sannella
  • Published 2018
  • Mathematics
  • arXiv: Representation Theory
  • Following Craven and Rouquier's computational method to tackle Brou\'e's abelian defect group conjecture, we present two algorithms implementing that procedure in the case of principal blocks of defect $D \cong C_{\ell} \times C_{\ell}$ for a prime $\ell$; the first describes a stable equivalence between $B_0(G)$ and $B_0(N_G(D))$, and the second tries to lift a such stable equivalence to a perverse derived equivalence. As an application, we show that Brou\'e's conjecture holds for the… CONTINUE READING

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