The index of centralizers of elements of reductive Lie algebras

Details The index of centralizers of elements of reductive Lie algebras The index of centralizers of elements of reductive Lie algebras

2010-05-05

arxiv.org/abs/1005.0831v1

Documenta Mathematica 15 (2010) 347-380

Mathematics

Representation Theory

28 pages in English

Scientific paper

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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