Minimal inversion complete sets and maximal abelian ideals

Abstract

Let $\mathfrak{g}$ be a simple Lie algebra, $\mathfrak{b}$ a fixed Borel subalgebra, and $W$ the Weyl group of $\mathfrak{g}$. In this note, we study a relationship between the maximal abelian ideals of $\mathfrak{b}$ and the minimal inversion complete sets of $W$. The latter have been recently defined by Malvenuto et al. (J. Algebra, 424 (2015), 330-356.)

17 pages

Cited by in corpus (2)

• Abelian ideals of a Borel subalgebra and root systems, II
• Normalisers of abelian ideals of a Borel subalgebra and $\mathbb{Z}$-gradings of a simple Lie algebra