Hu's generalized surjectivity conjecture for symplectic Schur–Weyl duality

Let $K$ be any field, let $V_K$ be the corresponding symplectic module, and let $\mathfrak{B}_{n,K}$ be the Brauer algebra with ideal $\mathfrak{B}_{n,K}^{(f)}$. For an integer $f$ with $0\leq f\leq [n/2]$, write

$$S_K^{sy}(m,n)=\operatorname{End}_{\mathfrak{B}_{n,K}}(V_K^{\otimes n})$$

and consider the natural map

$$\psi'_{f,K}:S_K^{sy}(m,n)\longrightarrow \operatorname{End}_{\mathfrak{B}_{n,K}}\bigl(V_K^{\otimes n}/V_K^{\otimes n}\mathfrak{B}_{n,K}^{(f)}\bigr).$$

Hu's generalized surjectivity conjecture. The natural map $\psi'_{f,K}$ is surjective. The paper states that this conjecture implies the preceding algebraically closed-field conjecture, extending the proposed surjectivity to arbitrary fields.