Ideals of Heisenberg type and minimax elements of affine Weyl groups

Details Ideals of Heisenberg type and minimax elements of affine Weyl groups Ideals of Heisenberg type and minimax elements of affine Weyl groups

2003-11-20

arxiv.org/abs/math/0311347v1

Mathematics

Representation Theory

25 pages

Scientific paper

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 Heisenberg ideal. The Heisenberg ideal is the nilpotent radical of the centralizer of the highest root vector. Second, we study the ideals having the property that the corresponding domain of the Shi arrangement consists of a single alcove. Such ideals (and the corresponding elements of the affine Weyl group) are called minimax.

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