Symmetries of stochastic colored vertex models

2020/03/13 by Galashin, Pavel
#05E99 #14M15 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 82C22. Secondary: 60K35 #Probability (math.PR)

paper · doi:10.48550/arxiv.2003.06330

Abstract

We discover a new property of the stochastic colored six-vertex model called flip-invariance. We use it to show that for a given collection of observables of the model, any transformation that preserves the distribution of each individual observable also preserves their joint distribution. This generalizes recent shift-invariance results of Borodin-Gorin-Wheeler. As limiting cases, we obtain similar statements for the Brownian last passage percolation, the Kardar-Parisi-Zhang equation, the Airy sheet, and directed polymers. Our proof relies on an equivalence between the stochastic colored six-vertex model and the Yang-Baxter basis of the Hecke algebra. We conclude by discussing the relationship of the model with Kazhdan-Lusztig polynomials and positroid varieties in the Grassmannian.

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