Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field

Abstract: Stable spin Hall-Littlewood symmetric polynomials labeled by partitions were recently introduced by Borodin and Wheeler in the context of higher spin six vertex models, which are one-parameter deformation of the Hall-Littlewood polynomials. We present a new combinatorial definition for the stable spin Hall-Littlewood polynomials, and derive a series of new combinatorial identities, including the skew Littlewood identity, refined Cauchy identity and refined Littlewood identity. Employing bijectivisation of summation identities, Bufetov and Petrov introduced local stochastic moves based on the Yang-Baxter equation. Combining the skew Littlewood identity and these moves, we introduce the half-space Yang-Baxter random field for stable spin Hall-Littlewood polynomials. We match the lengths of the partitions in this field with a new dynamic version of stochastic six vertex model in the half-quadrant, which can be mapped to a dynamic version of discrete-time interacting particle system on the half-line with an open boundary.