Yang-Baxter field for spin Hall-Littlewood symmetric functions

TL;DR

This paper introduces a new probabilistic model called the spin Hall-Littlewood Yang-Baxter field, based on the Yang-Baxter equation, which generalizes existing models like the stochastic six vertex model and ASEP.

Contribution

It develops a novel stochastic framework using Yang-Baxter moves for spin Hall-Littlewood functions, connecting them with particle configurations and extending known integrable models.

Findings

Defined the spin Hall-Littlewood Yang-Baxter field as a new probabilistic object.

Established connections between the field and spin Hall-Littlewood processes.

Derived degenerations leading to dynamic stochastic six vertex and ASEP models.

Abstract

Employing bijectivisation of summation identities, we introduce local stochastic moves based on the Yang-Baxter equation for $U_q(\widehat{\mathfrak{sl}_2})$. Combining these moves leads to a new object which we call the spin Hall-Littlewood Yang-Baxter field - a probability distribution on two-dimensional arrays of particle configurations on the discrete line. We identify joint distributions along down-right paths in the Yang-Baxter field with spin Hall-Littlewood processes, a generalization of Schur processes. We consider various degenerations of the Yang-Baxter field leading to new dynamic versions of the stochastic six vertex model and of the Asymmetric Simple Exclusion Process.