Stochastic six-vertex models, Hall-Littlewood positivity and $t$-deformed Schensted insertions

TL;DR

This paper establishes a positivity theorem for operators derived from the stochastic six-vertex model and explores their connections with other vertex models and $t$-deformed Schensted insertions, revealing new algebraic and combinatorial insights.

Contribution

It introduces a new positivity result for operators linked to the stochastic six-vertex model and connects it with $t$-deformed Schensted insertions, advancing understanding of these algebraic structures.

Findings

Proved a positivity theorem for certain operators in the stochastic six-vertex model.

Linked the positivity result to $t$-deformed Schensted insertions.

Explored connections with other vertex models.

Abstract

We prove a positivity theorem for a certain family of operators defined in terms of the stochastic six-vertex model. We explore connections of this result with other vertex models and $t$-deformed Schensted insertions.