Decomposition of Hypergeometric SLE and Reversibility

Abstract

In this paper, we consider hypergeometric SLE process for $\kappa\in (4,8)$ and $\nu>\frac{\kappa}{2}-6$. Though the definition of hypergeometric SLE process is complicated, we show that given its hitting point on a specific boundary, its conditional law can be described by SLE$_\kappa(\underline\rho)$ process. Based on this observation, by constructing a pair of curves, we derive the reversibility of hypergeometric SLE for $\kappa\in(4,8)$ and $\nu>-2$.