On construction of maximal parabolic centralizers of root elements and the Weyl group of type F4 in E6(K) for fields K of characteristic 2
The purpose of this paper is to give an elementary and explicit construction of maximal parabolic centralizers of root elements in the Chevalley group E₆(K), and to show that the centralizer of a Seigel involution in the Weyl group W of type E₆(K) is the Weyl group of type F₄, or equivalently, it is...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-10-01
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| Series: | Kuwait Journal of Science |
| Subjects: | |
| Online Access: | https://www.sciencedirect.com/science/article/pii/S2307410823001177 |
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| Summary: | The purpose of this paper is to give an elementary and explicit construction of maximal parabolic centralizers of root elements in the Chevalley group E₆(K), and to show that the centralizer of a Seigel involution in the Weyl group W of type E₆(K) is the Weyl group of type F₄, or equivalently, it is the stabilizer of a totally singular line L in W, using properties of the generalized quadrangle of type (2).
The construction here of the maximal parabolic centralizers of root elements in E₆(K) for fields K of characteristic 2 is somewhat novel, beginning as it does with root bases of Levi-type and root bases of unipotent type, giving an explicit construction of the group generated by these two types. |
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| ISSN: | 2307-4116 |