Ideals of Heisenberg type and minimax elements of affine Weyl groups
Representation Theory
2007-05-23 v1 Combinatorics
Abstract
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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Cite
@article{arxiv.math/0311347,
title = {Ideals of Heisenberg type and minimax elements of affine Weyl groups},
author = {Dmitri I. Panyushev},
journal= {arXiv preprint arXiv:math/0311347},
year = {2007}
}
Comments
25 pages