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2009•arXiv (Cornell University)Open access

On unipotent and nilpotent pieces

Ting Xue

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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 (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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What this paper is about

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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Available 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 (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.

Key concepts: Unipotent, Nilpotent, Mathematics, Pure mathematics, Nilpotent matrix, Closure (psychology), Nilpotent group, Set (abstract data type)

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