On sheets of conjugacy classes in good characteristic

Details On sheets of conjugacy classes in good characteristic On sheets of conjugacy classes in good characteristic

2010-11-26

arxiv.org/abs/1011.5791v2

Mathematics

Representation Theory

After acceptance and typesetting of the journal version of the paper, we discovered that the notions of Levi envelope, Jordan

Scientific paper

10.1093/imrn/rnr047

We show that the sheets for a connected reductive algebraic group G over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with G-conjugacy classes of triples (M, Z(M)^\circ t, O) where M is the connected centralizer of a semisimple element in G, Z(M)^\circ t is a suitable coset in Z(M)/Z(M)^\circ and O is a rigid unipotent conjugacy class in M. Any semisimple element is contained in a unique sheet S and S corresponds to a triple with O={1}. The sheets in G containing a unipotent conjugacy class are precisely those corresponding to triples for which M is a Levi subgroup of a parabolic subgroup of G and such a class is unique.

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