Imaginary geometry II: reversibility of SLE_\kappa(\rho_1;\rho_2) for \kappa \in (0,4)

Understand

Given a simply connected planar domain D, distinct points x,y \in \partial D, and \kappa >0, the Schramm-Loewner evolution SLE_\kappa is a random continuous non-self-crossing path in the closure of D from x to y.

• The SLE_\kappa(\rho_1;\rho_2) processes, defined for \rho_1, \rho_2 > -2, are in some sense the most natural generalizations of SLE_\kappa.
• When \kappa \leq 4, we prove that the law of the time-reversal of an \SLE_\kappa(\rho_1;\rho_2) from x to y is, up to parameterization, an SLE_\kappa(\rho_2;\rho_1) from y to x.
• This assumes that the "force points" used to define SLE_\kappa(\rho_1;\rho_2) are immediately to the left and right of the SLE seed.