The null-vector characterization of ideals in symplectic reflection algebras

Let $H_{1,\eta}(A_{n-1})$ be the symplectic reflection algebra, and let $sp$ be a $\varkappa$-trace on it. The bilinear form associated with $sp$ is

$$B_{sp}(f,g):=sp(fg)$$

for $f,g\in H_{1,\eta}(A_{n-1})$. Its null-vectors are the elements $v$ such that $B_{sp}(v,x)=0$ for every $x\in H_{1,\eta}(A_{n-1})$.

Null-vector characterization conjecture. Each ideal of $H_{1,\eta}(A_{n-1})$ is the set of null-vectors of the degenerate bilinear form $B_{sp}$ for some $\varkappa$-trace $sp$ on $H_{1,\eta}(A_{n-1})$.

This would characterize all ideals of these algebras through degenerate trace-induced bilinear forms. The surrounding discussion records the relationship between such null-vector ideals and known simplicity results, but does not establish the assertion for every ideal.