Symmetric pairs and associated commuting varieties

Details Symmetric pairs and associated commuting varieties Symmetric pairs and associated commuting varieties

2006-01-22

arxiv.org/abs/math/0601534v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

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.

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