Derived equivalences and equivariant Jordan decomposition

Ruhstorfer, Lucas

doi:10.1090/ert/605

Derived equivalences and equivariant Jordan decomposition
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by Lucas Ruhstorfer

Represent. Theory 26 (2022), 542-584

DOI: https://doi.org/10.1090/ert/605

Published electronically: April 27, 2022

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Abstract:

The Bonnafé–Rouquier equivalence can be seen as a modular analogue of Lusztig’s Jordan decomposition for groups of Lie type. In this paper, we show that this equivalence can be lifted to include automorphisms of the finite group of Lie type. Moreover, we prove the existence of a local version of this equivalence which satisfies similar properties.

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