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.

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

References in corpus (5)

• Component groups of unipotent centralizers in good characteristic
• From conjugacy classes in the Weyl group to unipotent classes
• On a Dimension Formula for Twisted Spherical Conjugacy Classes in Semisimple Algebraic Groups
• Strictly transversal slices to conjugacy classes in algebraic groups
• On conjugacy classes in a reductive group

Cited by in corpus (4)

• Masses, Sheets and Rigid SCFTs
• Lusztig's strata are locally closed
• Birational sheets in reductive groups
• Local geometry of Jordan classes in semisimple algebraic groups