On seaweed subalgebras and meander graphs in type D

Abstract

In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in ${\mathfrak{gl}}_n$ and computed their index using certain graphs, which we call type-$\mathsf{A}$ meander graphs. Then the subalgebras of seaweed type, or just "seaweeds", have been defined by Panyushev (2001) for arbitrary reductive Lie algebras. Recently, a meander graph approach to computing the index in types $\mathsf{B}$ and $\mathsf{C}$ has been developed by the authors. In this article, we consider the most difficult and interesting case of type $\mathsf{D}$. Some new phenomena occurring here are related to the fact that the Dynkin diagram has a branching node.

23 pages

References in corpus (2)

• Index and stable linear forms of Lie algebras
• On seaweed subalgebras and meander graphs in type C

Cited by in corpus (3)

• The index and spectrum of Lie poset algebras of type B, C, and D
• Indice des sous-algèbres biparaboliques d'une algèbre de Lie simple classique
• Existence of Richardson elements in seaweed Lie algebras of type $\mathbb{B}$, $\mathbb{C}$ and $\mathbb{D}$