On spherical twisted conjugacy classes
Representation Theory
2012-10-02 v3 Group Theory
Abstract
Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. We generalize to good odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy classes.
Cite
@article{arxiv.1104.0216,
title = {On spherical twisted conjugacy classes},
author = {Giovanna Carnovale},
journal= {arXiv preprint arXiv:1104.0216},
year = {2012}
}
Comments
proof of Lemma 6.4 polished. The journal version is available at http://www.springerlink.com/content/k573l88256753640/