Skip to Main content Skip to Navigation
Journal articles

Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs

Abstract : The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of Popov. In [Po], the irregular locus of the commuting variety of any reductive Lie algebra is described and its codimension is computed. This provides a bound for the codimension of the singular locus of this commuting variety. [Po, Remark 1.13] suggests that the arguments and methods of [Po] are suitable for obtaining analogous results in the symmetric setting. We show that some difficulties arise in this case and we obtain some results on the irregular locus of the component of maximal dimension of the "symmetric commuting variety". As a by-product, we study some pairs of commuting elements specific to the symmetric case, that we call rigid pairs. These pairs allow us to find all symmetric Lie algebras whose commuting variety is reducible.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00660569
Contributor : Michael Bulois <>
Submitted on : Tuesday, January 17, 2012 - 9:56:04 AM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
Document(s) archivé(s) le : Wednesday, April 18, 2012 - 2:32:24 AM

Files

irregular_locus34.pdf
Files produced by the author(s)

Identifiers

Citation

Michael Bulois. Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs. Transformation Groups, Springer Verlag, 2011, 16 (4), pp.1027-1061. ⟨10.1007/s00031-011-9162-5⟩. ⟨hal-00660569⟩

Share

Metrics

Record views

634

Files downloads

359