Existence of Richardson elements in seaweed Lie algebras of type $\mathbb{B}$, $\mathbb{C}$ and $\mathbb{D}$

The main result of this paper is the existence of Richardson elements for seaweed (biparabolic) Lie algebras of type $\mathbb{B, C}$ and $\mathbb{D}$. We develop non-trivial conditions on stabilisers that are sufficient for the existence of Richardson elements and then verify these conditions using quiver representation theory.