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arXiv · 1702.07879

On seaweed subalgebras and meander graphs in type D

Dmitri Panyushev·Oksana Yakimova
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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-${\sf A}$ 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 ${\sf B}$ and ${\sf C}$ has been developed by the authors. In this article, we consider the most difficult and interesting case of type ${\sf D}$. Some new phenomena occurring here are related to the fact that the Dynkin diagram has a branching node.

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BibTeXRIS

Dmitri Panyushev, Oksana Yakimova. 2017-02-25. On seaweed subalgebras and meander graphs in type D. https://doi.org/10.1016/j.jpaa.2017.12.015

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