  Fully inhomogeneous spin Hall-Littlewood symmetric rational functions
$F_\lambda$ are multiparameter deformations of the classical Hall-Littlewood
symmetric polynomials and can be viewed as partition functions in
$\mathfrak{sl}(2)$ higher spin six vertex models. We obtain a refined
Littlewood identity expressing a weighted sum of $F_\lambda$'s over all
partitions $\lambda$ with even multiplicities as a certain Pfaffian. This
Pfaffian can be derived as a partition function of the six vertex model in a
triangle with suitably decorated domain wall boundary conditions. The proof is
based on the Yang-Baxter equation.
