Ideals of Heisenberg type and minimax elements of affine Weyl groups
Dmitri I. Panyushev
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.
Create a lesson
Related papers
Arthur packets for G2 over p-adic fields
Yugo Takanashi
Representation embeddings and the third Brauer--Thrall conjecture
Haruhisa Enomoto
Non-admissible smooth irreducible representations of GL2(F) for totally ramified extensions F/Qp
Dayu Huang
Stable equivalence of quadratic monomial algebras
Pengyun Chen, Bohan Xing
Root vector localization and minimal nilpotent finite W-algebras
Genqiang Liu
Lusztig sheaves, local systems, and the extended Springer resolution
William Graham, Martha Precup, Amber Russell