On Lusztig's map for spherical unipotent conjugacy classes
Representation Theory
2014-02-26 v2 Group Theory
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.
Cite
@article{arxiv.1210.0223,
title = {On Lusztig's map for spherical unipotent conjugacy classes},
author = {Giovanna Carnovale and Mauro Costantini},
journal= {arXiv preprint arXiv:1210.0223},
year = {2014}
}
Comments
Refereed version, one reference added. The final version will appear in the Bulletin of the London Mathematical Society