On seaweed subalgebras and meander graphs in type D

In 2000, Dergachev and Kirillov introduced subalgebras of “seaweed type” in gln and computed their index using certain graphs, which we call type-A meander graphs. Then the subalgebras of seaweed type, or just “seaweeds”, have been defined by Panyushev (2001) [9] for arbitrary reductive Lie algebras. Recently, a meander graph approach to computing the index in types B and C has been developed by the authors. In this article, we consider the most difficult and interesting case of type D. Some new phenomena occurring here are related to the fact that the Dynkin diagram has a branching node.