On unipotent and nilpotent pieces for classical groups

Abstract

We show that the definition of unipotent (resp. nilpotent) pieces for classical groups given by Lusztig (resp. Lusztig and the author) coincides with the combinatorial definition using closure relations on unipotent classes (resp. nilpotent orbits). Moreover we give a closed formula for a map from the set of unipotent classes (resp. nilpotent orbits) in characteristic 2 to the set of unipotent classes in characteristic 0 such that the fibers are the unipotent (resp. nilpotent) pieces.

19 pages

References in corpus (3)

• From conjugacy classes in the Weyl group to unipotent classes
• Combinatorics of the Springer correspondence for classical Lie algebras and their duals in characteristic 2
• Pieces of nilpotent cones for classical groups

Cited by in corpus (2)

• Pieces of nilpotent cones for classical groups
• $q$-Kreweras numbers for coincidental Coxeter groups attached to limit symbols