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The index of a Lie algebra $\mathfrak{g}$ is defined by ind $\mathfrak{g}=$$\min_{f\in \mathfrak{g}^*}\dim(\ker (B_f))$, where $f$ is an element of thelinear dual $\mathfrak{g}^*$ and $B_f(x,y)=f([x,y])$ is the associatedskew-symmetric Kirillov form. We develop a broad general framework for theexplicit construction of regular (index realizing) functionals for seaweedsubalgebras of $\mathfrak{gl}(n)$ and the classical Lie algebras:$A_n=\mathfrak{sl}(n+1),$ $B_n=\mathfrak{so}(2n+1)$, and$C_n=\mathfrak{sp}(2n)$. Until now, this problem has remained open in$\mathfrak{gl}(n)$ -- and in all the classical types.

Regular functionals on seaweed Lie algebras