Decomposition varieties in semisimple Lie algebras
Printed: Oct 1998
The notion of decompositon class in a semisimple Lie algebra is a
common generalization of nilpotent orbits and the set of
regular semisimple elements. We prove that the closure of a
decomposition class has many properties in common with nilpotent
varieties, \eg, its normalization has rational singularities.
The famous Grothendieck simultaneous resolution is related to the
decomposition class of regular semisimple elements. We study the
properties of the analogous commutative diagrams associated to
an arbitrary decomposition class.
14L30 - Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
14M17 - Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
15A30 - Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
17B45 - Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]