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math.RT2003
Ideals of Heisenberg type and minimax elements of affine Weyl groups
Dmitri I. Panyushev
We consider ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra. The goal of this paper is two-fold. First, we study the ad-nilpotent ideals lying inside the Heisenbe…
math.RT2003
Long Abelian ideals
Dmitri I. Panyushev
We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the…
math.RT2003★ 1 cited
Ad-nilpotent ideals of a Borel subalgebra: generators and duality
Dmitri I. Panyushev
It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and t…