Symmetries of stochastic colored vertex models

Pavel Galashin

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arXiv · 2003.06330

Symmetries of stochastic colored vertex models

Pavel Galashin

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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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Pavel Galashin. 2020-03-13. Symmetries of stochastic colored vertex models. https://arxiv.org/abs/2003.06330

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