The finite W-algebra structure of noncommutative pfaffians

Let $\mathfrak{o}_N$ be the orthogonal Lie algebra with generators $F_{ij}=E_{ij}-E_{ji}$, and let $PfF_I$ denote the noncommutative pfaffian of the skew-symmetric submatrix $F_I=(F_{i,j})_{i,j\in I}$ for an index set $I\subset\{1,\ldots,N\}$. These pfaffians satisfy commutation relations inside $U(\mathfrak{o}_N)$, and the sums of their squares give central elements. Pfaffian algebra question. What kind of algebraic object do the pfaffians form? Is it isomorphic to a finite $W$-algebra? The question arises from the commutation relations among the pfaffians and their relationship with central elements of $U(\mathfrak{o}_N)$; the source does not specify a proposed isomorphism or a resolution.