Ad-Nilpotent Ideals of a Parabolic Subalgebra

Details Ad-Nilpotent Ideals of a Parabolic Subalgebra Ad-Nilpotent Ideals of a Parabolic Subalgebra

2007-01-24

arxiv.org/abs/math/0701679v2

Mathematics

Representation Theory

Proof of 4.1 corrected and generalized to all types. Further references and remarks added

Scientific paper

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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