From conjugacy classes in the Weyl group to unipotent classes, III

By G. Lusztig. 2011

78 citations recorded by the source corpus.

Let G be an affine algebraic group over an algebraically closed field such that the identity component G^0 of G is reductive. Let W be the Weyl group of G and let D be a connected component of G whose image in G/G^0 is a unipotent element. In this paper we define a map from the set of "twisted conjugay classes" in W to the set of unipotent G^0-conjugacy classes in D, generalizing an earlier construction which applied when G is connected.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/caf115d7f94ab51ae18a98a2d3f436ff135d5907

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In Geometry and Topology

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Citations in the corpus

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras (2012, background): “Lusztig (see [13] and the references therein) has had a series of papers explaining how the cases of bad characteristic can be understood.”
Motives with exceptional Galois groups and the inverse Galois problem (2011, background): “(Qℓ) →Gb(Fℓ) is surjective. This solves the inverse Galois problem for the ﬁnite simple group Gb(Fℓ). 4.6. Conjectural properties of the local system. 4.6.1. Local monodromy. Lusztig has deﬁned a map [L10] {conjugacy classes in W}→{unipotent classes in Gb} In particular, if −1 ∈Wgets mapped to a uni”
The development version of the CHEVIE package of GAP3 (2013, unknown): “1] describing the same computation. The problem is very easy to solve using the development version of CHEVIE, as we will show by giving the complete code to solve it; Lusztig notes in an addendum in [Lusztig2011b] that Theorem 4 still holds in bad characteristic for exceptional groups. Our code wil”