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Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions
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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
????????
(
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.
Title: Refined Littlewood identity for spin Hall–Littlewood symmetric rational functions
Description:
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
????????
(
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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