SLE martingales and the Virasoro algebra

Details SLE martingales and the Virasoro algebra SLE martingales and the Virasoro algebra

2003-01-10

arxiv.org/abs/hep-th/0301064v2

Phys.Lett.B557:309-316,2003

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, to appear in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(03)00189-8

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.

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