Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions

Abstract

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 sl(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.