SLE(\kappa,\rho) martingales and duality

Various features of the two-parameter family of Schramm-Loewner evolutions SLE(\kappa,\rho) are studied. In particular, we derive certain restriction properties that lead to a ``strong duality’’ conjecture, which is an identity in law between the outer boundary of a variant of the SLE(\kappa) process for \kappa \ge 4 and a variant of the SLE(16/\kappa) process.