# Ad-nilpotent Ideals and Equivalence Relations - Mathematics > Representation Theory

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Abstract: In this paper we study ad-nilpotent ideals of a complex simple Lie algebra$\ccg$ and their connections with affine Weyl groups and nilpotent orbits. Wedefine a left equivalence relation for ad-nilpotent ideals based on theirnormalizer and generators, and prove that the equivalence relation iscompatible with the left cell structure of affine Weyl group of $\ccg$ andLusztig-s star operator for type $\tilde A {n-1}$.

Autor: Chuying Fang

Fuente: https://arxiv.org/