Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions

Fully inhomogeneous spin Hall–Littlewood symmetric rational functions F λ are multiparameter deformations of the classical Hall–Littlewood symmetric polynomials and can be viewed as partition functions in ???????? ( 2 ) higher spin six vertex models. We obtain a refined Littlewood identity expressing a weighted sum of F λ ’s over all signatures λ 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.