On related varieties to the commuting variety of a semisimple Lie algebra

Details On related varieties to the commuting variety of a semisimple Lie algebra On related varieties to the commuting variety of a semisimple Lie algebra

2011-05-30

arxiv.org/abs/1105.5921v2

Mathematics

Representation Theory

29 pages. Reference added

Scientific paper

Let g be a semisimple Lie algebra of finite dimension. The nullcone N of g is
the set of (x,y) in g x g such that x and y are nilpotents and are in the same
Borel sualgebra. The main result of this paper is that N is a closed and
irreducible subvariety of g x g, its normalisation has rational singularities
and its normalization morphism is bijective.

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