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 $\nu >-2$.

13 pages, 1 figure