Springer’s work on unipotent classes and Weyl group representations
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.
متن کاملElliptic Weyl Group Elements and Unipotent Isometries
Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...
متن کاملFrom Conjugacy Classes in the Weyl Group to Unipotent Classes, Ii
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...
متن کاملFrom Conjugacy Classes in the Weyl Group to Unipotent Classes, Iii
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...
متن کاملELLIPTIC WEYL GROUP ELEMENTS AND UNIPOTENT ISOMETRIES WITH p = 2
Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class Φ(C) of G. In this paper we show that Φ(C) can be characterized in terms of the closure relations between unipotent classes. Previously, the analogous result was known ...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2020
ISSN: 0019-3577
DOI: 10.1016/j.indag.2020.08.007