From conjugacy classes in the Weyl group to unipotent classes, III
نویسندگان
چکیده
منابع مشابه
From Conjugacy Classes in the Weyl Group to Unipotent Classes
Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes in G.
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Let G be an affine algebraic group over an algebraically closed field whose identity component G0 is reductive. Let W be the Weyl group of G and let D be a connected component of G whose image in G/G0 is unipotent. In this paper we define a map from the set of “twisted conjugacy classes” in W to the set of unipotent G0-conjugacy classes in D generalizing an earlier construction which applied wh...
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Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map Φp from the set W of conjugacy classes in the Weyl group W to the set of unipotent classes in G. Here we prove three results for Φp. First we show that Φp has a canonical one-sided inverse. Next we show that Φ0 = rΦp for a unique map r. Finally, we constru...
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Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra G ⊗ C[λ, λ −1 ] are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group W(G) of the simple Lie algebra G. A representative w ∈ W(G) of a regular c...
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We define and study a correspondence between the set of distinguished G0-conjugacy classes in a fixed connected component of a reductive group G (with G0 almost simple) and the set of (twisted) elliptic conjugacy classes in the Weyl group. We also prove a homogeneity property related to this correspondence. Introduction 0.1. Let k be an algebraically closed field of characteristic p ≥ 0 and let...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2012
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-2012-00422-8