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Ad-Nilpotent Ideals of a Parabolic Subalgebra

Céline Righi
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Abstract

We extend the results of Cellini-Papi on the characterizations of nilpotent and abelian ideals of a Borel subalgebra to parabolic subalgebras of a simple Lie algebra. These characterizations are given in terms of elements of the affine Weyl group and faces of alcoves. In the case of a parabolic subalgebra of a classical Lie algebra, we give formulas for the number of these ideals.

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Céline Righi. 2007-11-05. Ad-Nilpotent Ideals of a Parabolic Subalgebra. https://arxiv.org/abs/math/0701679

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