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arXiv · 2104.09755

Refined Littlewood identity for spin Hall-Littlewood symmetric rational functions

Svetlana Gavrilova
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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.

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Svetlana Gavrilova. 2021-04-20. Refined Littlewood identity for spin Hall-Littlewood symmetric rational functions. https://arxiv.org/abs/2104.09755

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