Quasi-Isolated Elements in Reductive Groups

By C'edric Bonnaf'e. 2004

84 citations recorded by the source corpus.

Abstract A semisimple element s of a connected reductive group G is called quasi-isolated (respectively isolated) if C G ( s ) (respectively ( s )) is not contained in a Levi subgroup of a proper parabolic subgroup of G . We study properties of quasi-isolated semisimple elements and give a classification in terms of the affine Dynkin diagram of G . Tables are provided for adjoint simple groups.

Subfields: Geometry and Topology, Inorganic Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a208fa8150a01f45eb74eed6bee4cd6ff96ffde

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In Geometry and Topology

In Inorganic Chemistry

In Mathematical Physics

Citations in the corpus

2-blocks with abelian defect groups (2013, unknown): “The identity is the only quasi-isolated element of odd order in G, (see for example table 2 of [2]), hence s = 1 and B is unipotent.”
Characters of odd degree (2015, unknown): “The conjugacy classes of quasi-isolated elements s in classical groups of adjoint type were classiﬁed in [Bon05, Tab.”
Computational proof of the Mackey formula for q>2 (2010, methodology): “The algorithm to get these was described in [4].”
The development version of the CHEVIE package of GAP3 (2013, methodology): “The algorithm to get these was described in [Bonnafe2005].”
Brauer's Height Zero Conjecture (2022, background): “The element s and its centralizer in G ∗ are described in terms of root systems in [3]. e e e Since e G ⋊ D induces Aut( G ) and [13, Thm 3.1] tells us Jordan decomposition for e G can be chosen to be D -equivariant, we then obtain as in the proof of Proposition 3.16 two non-Aut( G )-conjugate…”