Refined Littlewood identity for spin Hall-Littlewood symmetric rational functions

Abstract

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.

15 pages, 20 figures; typos corrected, references added