Symmetries of stochastic colored vertex models

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