Ad-Nilpotent Ideals of a Parabolic Subalgebra
Abstract
Description
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.
Proof of 4.1 corrected and generalized to all types. Further references and remarks added
Proof of 4.1 corrected and generalized to all types. Further references and remarks added