Lusztig's partition and sheets (with an appendix by M. Bulois)
Abstract
We show that, for a connected reductive algebraic group G over an algebraically closed field of zero or good characteristic, the parts, called strata, in the partition of G recently introduced by Lusztig are unions of sheets of conjugacy classes. For G simple and adjoint we refine the parametrization of such sheets obtained in previous work with F. Esposito. We give a simple combinatorial description of strata containing spherical conjugacy classes, showing that Lusztig's correspondence induces a bijection between unions of spherical conjugacy classes and unions of classes of involutions in the Weyl group. Using ideas from the Appendix by M. Bulois, we show that the closure of a stratum is not necessarily a union of strata.
Keywords
Cite
@article{arxiv.1307.8302,
title = {Lusztig's partition and sheets (with an appendix by M. Bulois)},
author = {G. Carnovale},
journal= {arXiv preprint arXiv:1307.8302},
year = {2015}
}
Comments
New results are added: we show that strata are locally closed in Corollary 2.2. Section 5 is enhanced, and we show that Lusztig's correspondence restricts to unions of spherical classes on the algebraic group side and unions of classes of involutions on the Weyl group side. The file includes arXiv:1011.5045 as an Appendix