Ad-Nilpotent Ideals of a Parabolic Subalgebra

2007/01/24 by Righi, Céline
#17B20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0701679

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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