Ad-nilpotent Ideals of Minimal Dimension

Details Ad-nilpotent Ideals of Minimal Dimension Ad-nilpotent Ideals of Minimal Dimension

2008-10-25

arxiv.org/abs/0810.4601v1

Mathematics

Representation Theory

Scientific paper

n this paper we study ad-nilpotent ideals of a complex simple Lie algebra $\ccg$ and their connections with affine Weyl groups and nilpotent orbits. We define a left equivalence relation for ad-nilpotent ideals based on their normalizer and generators, and prove that the equivalence relation is compatible with the left cell structure of affine Weyl group of $\ccg$ and Lusztig's star operator for type $\tilde A_{n-1}$.

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