The conjectural norm formula for Jack superpolynomials

Let $\Lambda$ be a superpartition, let ${P}^{(\alpha)}_\Lambda$ be the corresponding Jack superpolynomial, and let $B_i\Lambda$ for $i=0,1,2,3$ denote the four subsets of bosonic boxes defined by the terminal decorations of their rows and columns. Write $\Lambda^{[i]}$ for the associated partitions, let $M_3$ be the number of fermionic variables in the third sector, and let $\xi_{\overline{\underline{\Lambda}}}$ denote the normalization factor. For a partition $\lambda$ and its conjugate $\lambda'$, and a box $s=(i,j)$, define the arm-length and leg-length by

$$a_\lambda(s)=\lambda_i-j,\qquad \ell_\lambda(s)=\lambda'_j-i.$$

The norm conjecture. The superpolynomial ${P}^{(\alpha)}_\Lambda$ has norm, with respect to the combinatorial scalar product, given by

$$j_\Lambda:=\langle\!\langle {P}^{(\alpha)}_\Lambda\mid {P}^{(\alpha)}_\Lambda\rangle\!\rangle_\alpha=\frac{\alpha^{M_3}}{\xi_{\overline{\underline{\Lambda}}}}\prod_{i=0}^{3}\prod_{s\in B_i\Lambda}\frac{\ell_{\Lambda^{[i-1]}(s)}+(a_{\Lambda^{[0]}(s)}+1)\alpha}{\ell_{\Lambda^{[i]}(s)}+1+a_{\Lambda^{[3]}}(s)\alpha},$$

with the convention $\Lambda^{[-1]}\equiv\Lambda^{[3]}$. This formula gives the conjectured combinatorial norm of Jack superpolynomials and extends the product formulas familiar from ordinary Jack polynomials; the supplied text does not state a proof or a resolution.