English

Descent of equivalences for blocks with Klein four defect groups

Group Theory 2021-10-18 v6 Representation Theory

Abstract

We show that the splendid Rickard complexes for blocks with Klein four defect groups constructed by Rickard and Linckelmann descend to non-split fields. As a corollary, Navarro's refinement of the Alperin-McKay conjecture holds for blocks with a Klein four defect group. We also prove that splendid Morita equivalences between blocks and their Brauer correspondents (if exist) descend to non-split situations.

Keywords

Cite

@article{arxiv.2106.03809,
  title  = {Descent of equivalences for blocks with Klein four defect groups},
  author = {Xin Huang},
  journal= {arXiv preprint arXiv:2106.03809},
  year   = {2021}
}

Comments

Corrected some misprints