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Simion, Iulian I.

Double centralizers of unipotent elements in simple algebraic groups of type \(E_7\) and \(E_8\). (English) Zbl 1306.20052

J. Pure Appl. Algebra 219, No. 4, 930-977 (2015).
Summary: This article addresses questions about the double centralizer \(C_G(C_G(u))=Z(C_G(u))\) of unipotent elements \(u\) in simple algebraic groups \(G\) of type \(E_7\) and \(E_8\) defined over algebraically closed fields of bad characteristic. We use the method developed in [I. I. Simion, J. Algebra 382, 335-367 (2013; Zbl 1286.20062)] to determine \(Z(C_G(u))^\circ\), deduce its dimension and recognize if it is an overgroup for \(u\). The method used requires explicit representatives of the component group of \(C_G(u)\) which we produce in all cases. This article extends the results of [loc. cit.] to all exceptional type groups.

Cited in 1 Document

MSC:

20G41 Exceptional groups
20E45 Conjugacy classes for groups

Keywords:

simple algebraic groups; unipotent elements; connected components; double centralizers; bad characteristic; exceptional groups

Citations:

Zbl 1286.20062

Software:

SageMath; GAP
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Full Text: DOI

References:

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