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Pré-Publication, Document De Travail Année : 2015

The index of centralizers of elements of reductive Lie algebras

Résumé

For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer of an element of a reductive Lie algebra is equal to the rank. That conjecture caught attention of several Lie theorists for years. In this paper we give an almost general proof of that conjecture.
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Dates et versions

hal-00375022 , version 1 (11-04-2009)
hal-00375022 , version 2 (04-05-2010)
hal-00375022 , version 3 (06-10-2015)
hal-00375022 , version 4 (16-10-2015)

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Jean-Yves Charbonnel, Anne Moreau. The index of centralizers of elements of reductive Lie algebras. 2015. ⟨hal-00375022v4⟩
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