Geodesic
Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions
Gavrilova, Svetlana1
1 National Research University Higher School of Economics Faculty of Mathematics 6 Usacheva st. Moscow 119048 (Russia)
Algebraic Combinatorics, Tome 6 (2023) no. 1, pp. 37-51

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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)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Gavrilova, Svetlana. Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions. Algebraic Combinatorics, Tome 6 (2023) no. 1, pp. 37-51. doi: 10.5802/alco.251

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