  We present an explicit relation between representations of the Virasoro
algebra and polynomial martingales in stochastic Loewner evolutions (SLE). We
show that the Virasoro algebra is the spectrum generating algebra of SLE
martingales. This is based on a new representation of the Virasoro algebra,
inspired by the Borel-Weil construction, acting on functions depending on
coordinates parametrizing conformal maps.
