SYMMETRIES OF STOCHASTIC COLORED VERTEX MODELS

• 成果类型: Article
• 署名作者: Galashin, Pavel
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1502
• 发表日期: 2021
• 页码: 2175-2219
• 关键词: level-spacing distributions; flag varieties; r-matrix; equation

摘要

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.