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Between the sheets: rigid nilpotent elements in modular Lie algebras

Presented by: 
David Stewart
Date: 
Tuesday 28th January 2020 - 14:45 to 15:35
Venue: 
INI Seminar Room 1
Abstract: 
(Joint with Sasha Premet) Let G be a reductive algebraic group over an algebraically closed field. Lusztig and Spaltenstein provided a method for inducing a nilpotent orbit from a Levi subgroup to the group G. Any orbit not obtained from a proper Levi subgroup is called rigid. These were classified by Kempken (for G classical) and Elashvili (for G exceptional). The latter was double-checked computationally by De Graaf. It turns out that this classification remains valid in characteristic p. I will explain the proof of this, obtained by extending the Borho-Kraft description of the sheets of the Lie algebra to positive characteristic and supported by a few computer calculations.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons