The fermionic-degree-one Macdonald superpolynomial conjugation conjecture

Let $\Lambda$ be a superpartition of fermionic degree $m=1$, let $H_\Lambda$ be the modified Macdonald superpolynomial, and let $\psi$ be the linear map defined on Schur superpolynomials by $\psi(s_\Omega)=s_{\Omega^{\circledast}}$. Conjugation conjecture. One has

$$\psi(H_\Lambda)=H_{\Lambda^{\circledast}}.$$

This conjecture predicts that the map induced by the circledast operation intertwines the corresponding modified Macdonald superpolynomials in fermionic degree one. The text presents it as a conjectural non-stable-sector statement, with stable-sector cases proved in the paper.