Symmetric pairs and associated commuting varieties

Abstract

We obtain a series of new results on the problem of irreducibility of commuting varieties associated with symmetric pairs or, in other words, $Z_2$-graded simple Lie algebras. In particular, we present many examples of reducible commuting varieties and show that the number of irreducible components can be arbitrarily large.

18 pages

References in corpus (1)

• Principal Nilpotent pairs in a semisimple Lie algebra, I

Cited by in corpus (8)

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• Differentiable stratified groupoids and a de Rham theorem for inertia spaces
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• Commuting involutions of Lie algebras, commuting varieties, and simple Jordan algebras
• Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs
• On pairs of commuting nilpotent matrices
• Sheets, slice induction and G2(2) case