Shift invariance of half space integrable models

Abstract

We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type B analogue of the oriented swap process and last passage times in a half space, establishing the Baik-Ben Arous-Péché phase transition for the absorption time. The proof uses Hecke algebras and integrability of the six vertex model through the Yang-Baxter and reflection equations.

Triangular solutions to the reflection equation for U q Kolyaskin, Mangazeev 2024J. Phys. A: Math. Theor.0000View full textAdd to dashboardCite

“…It is interesting to compare the obtained solutions (5.7) and (5.16) with already known results. In [35] the author introduced a solution to the reflection equation related to the stochastic R-matrix .20) derived in [36] through the fusion procedure. The solution from [35] has a similar structure to (5.7) and also includes the function Φ as a building block.…”