SLE local martingales, reversibility and duality

TL;DR

This paper investigates the properties of SLE local martingales, focusing on reversibility and duality, by leveraging the Virasoro algebra structure to compare processes at stopping times.

Contribution

It introduces an algebraic framework based on the Virasoro structure to analyze SLE reversibility and duality, providing new insights into their relationship.

Findings

Established algebraic conditions for SLE reversibility and duality.

Proved reversibility and duality for polynomial expected values under integrability.

Connected local martingale structures with Virasoro algebra representations.

Abstract

We study SLE reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic results showing that local martingales for the processes have enough in common. When one has in addition integrability, the method gives reversibility and duality for any polynomial expected value.