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arXiv · 1210.0223

On Lusztig's map for spherical unipotent conjugacy classes

Giovanna Carnovale·Mauro Costantini
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Abstract

We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztig's map Psi from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group. For irreducible root systems, we analyze the image of this restricted map and we prove that a conjugacy class in a finite Weyl group has a unique maximal length element if and only if it has a maximum.

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Giovanna Carnovale, Mauro Costantini. 2013-05-06. On Lusztig's map for spherical unipotent conjugacy classes. https://doi.org/10.1112/blms%2Fbdt048

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