Nakagawa–Naruse shifted reverse plane partition formulas for connective Schur functions

Let $\beta$ be a parameter, let $\beta$-dependent skew functions $g\hspace{-0.2mm}p_{ u}$ and $g\hspace{-0.2mm}q_{ u}$ be indexed by strict partitions, and let $u$ be a strict partition. For strict partitions $\mu\subseteq\lambda$, let ${\rm ShRPP}_Q(\lambda/\mu)$ be the set of shifted reverse plane partitions of shape $\lambda/\mu$, and let ${\rm ShRPP}_P(\lambda/\mu)$ be the \subset whose diagonal entries are all primed. For $T$ in either set, write $x^{\operatorname{wt}_{\rm RPP}(T)}$ for its row-and-column weight and $|\operatorname{wt}_{\rm RPP}(T)|$ for the degree of that weight. Nakagawa–Naruse's conjecture. If $\mu\subseteq\lambda$ are strict partitions, then

$$g\hspace{-0.2mm}p_{\lambda/\mu}=\sum_{T\in {\rm ShRPP}_P(\lambda/\mu)}(-\beta)^{|\lambda/\mu|-|\operatorname{wt}_{\rm RPP}(T)|}x^{\operatorname{wt}_{\rm RPP}(T)},$$

and

$$g\hspace{-0.2mm}q_{\lambda/\mu}=\sum_{T\in {\rm ShRPP}_Q(\lambda/\mu)}(-\beta)^{|\lambda/\mu|-|\operatorname{wt}_{\rm RPP}(T)|}x^{\operatorname{wt}_{\rm RPP}(T)}.$$

These formulas give conjectural generating functions for the skew connective Schur $P$- and $Q$-type functions; the source supplies no resolution status for this conjecture.