Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions
Algebraic Combinatorics, Volume 6 (2023) no. 1, pp. 37-51.

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.

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DOI: 10.5802/alco.251
Classification: 05E05, 82B20, 81R50
Keywords: Littlewood identity, symmetric functions, six vertex model
Gavrilova, Svetlana 1

1 National Research University Higher School of Economics Faculty of Mathematics 6 Usacheva st. Moscow 119048 (Russia)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Gavrilova, Svetlana. Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions. Algebraic Combinatorics, Volume 6 (2023) no. 1, pp. 37-51. doi : 10.5802/alco.251. https://alco.centre-mersenne.org/articles/10.5802/alco.251/

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