# Yang-Baxter field for spin Hall-Littlewood symmetric functions

### 2017/12/13

(with Alexey Bufetov)
arXiv:1712.04584 [math.PR]

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.

Forward transition probabilities associated with the Yang-Baxter field