Component groups of unipotent centralizers in good characteristic

Details Component groups of unipotent centralizers in good characteristic Component groups of unipotent centralizers in good characteristic

2002-04-23

arxiv.org/abs/math/0204275v2

Journal of Algebra 260 (2003) 323-337

Mathematics

Representation Theory

13 pages; AMS LaTeX. This is the final version; it will appear in the Steinberg birthday volume of the Journal of Algebra. Thi

Scientific paper

10.1016/S0021-8693(02)00661-0

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u in G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the second author done for simple, adjoint G over the complex numbers. When G is simple and adjoint, the previous work of the second author makes our description combinatorial and explicit; moreover, it turns out that knowledge of the conjugacy classes suffices to determine the group structure of A(u). Thus we obtain the result, previously known through case-checking, that the structure of the component group A(u) is independent of good characteristic.

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