Pieri rules for Macdonald polynomials in superspace

Let $P_\Lambda^{(q,t)}$ be the Macdonald polynomial in superspace indexed by a superpartition $\Lambda$, and let $e_n$ and $\tilde e_n$ denote the corresponding elementary symmetric functions. For superpartitions $\Lambda$ and $\Omega$, let $d(\Omega/\Lambda)$ be the integer defined from the word of labels associated with the skew diagram, and let $\psi'_{\Omega/\Lambda}$ and $\operatorname{Det}_{\Omega/\Lambda}$ be the factors from the Pieri coefficients, with

$$h_\Lambda^{(q,t)}(s)=1-t^{\ell_{\Lambda^\circledast}(s)}q^{a_{\Lambda^*}(s)+1},\qquad h^\Lambda_{(q,t)}(s)=1-t^{\ell_{\Lambda^*}(s)+1}q^{a_{\Lambda^\circledast}(s)}$$

and

$$[x;y]_{(q,t)}=\frac{(t-1)(q^{1/2}-q^{-1/2})}{(t^{(x-y)/2}-t^{-(x-y)/2})(q^{1/2}t^{(x-y)/2}-q^{-1/2}t^{-(x-y)/2})}.$$

Macdonald superspace Pieri-rule conjecture. The Pieri rules are

$$e_nP_\Lambda^{(q,t)}=\sum_\Omega v_{\Lambda\Omega}(q,t)P_\Omega^{(q,t)},\qquad \tilde e_nP_\Lambda^{(q,t)}=\sum_\Omega \tilde v_{\Lambda\Omega}(q,t)P_\Omega^{(q,t)},$$

where the sums range over $\Omega$ such that $\Omega/\Lambda$ is respectively a vertical $n$-strip or a vertical $\tilde n$-strip, and

v_{\Lambda\Omega}(q,t)=(-1)^{\\#(\Omega/\Lambda)}t^{d(\Omega/\Lambda)}\psi'_{\Omega/\Lambda}\operatorname{Det}_{\Omega/\Lambda},\qquad \tilde v_{\Lambda\Omega}(q,t)=(-1)^{\\#(\Omega/\Lambda)}t^{d(\Omega/\Lambda)}\psi'_{\Omega/\Lambda}\operatorname{Det}_{\Omega/\Lambda}.

The conjecture extends the Jack-polynomial Pieri rules to the two-parameter Macdonald setting in superspace; the stated coefficient factors are obtained by replacing the Jack hook and bracket quantities with their $(q,t)$ analogues. The supplied text gives no evidence of a proof or disproof, so its status remains open.