On unipotent and nilpotent pieces

Details On unipotent and nilpotent pieces On unipotent and nilpotent pieces

2009-12-18

arxiv.org/abs/0912.3820v3

Mathematics

Representation Theory

16 pages

Scientific paper

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 (resp. nilpotent) classes. Moreover we give a closed formula for a map from the set of unipotent (resp. nilpotent) classes in characteristic 2 to the set of unipotent classes in characteristic 0 such that the fibers are the unipotent (resp. nilpotent) pieces.

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