A Two-Color Lift of the Shifted $t$-Schur Measure

At the specialization $t=-q$, $q\geq0$, the shifted $t$-Schur function associated with the modified odd Greaves--Jing--Zhu operator is $Q_\lambda[X+qX]$. Instead of merging the two alphabets $X$ and $qX$, we insert an intermediate strict partition between the two corresponding half-vertex operators. This gives a two-color lift of the shifted Schur measure on pairs $\mu\subseteq\lambda$ with weight \[
Q_\mu(qX)Q_{\lambda/\mu}(X)P_\lambda(Y). \] We compute the normalization and both marginals, identify an explicit Markov transition kernel, prove a semigroup property, and show that the two color volumes $|\mu|$ and $|\lambda|-|\mu|$ are independent. We also realize the model as a two-time shifted Schur process and write its Pfaffian correlation kernel in Vuletić's convention. Rectangular specializations give closed formulas and Gaussian limits for the color volumes.