Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra
Abstract
We use the SLE loop measure to construct a natural representation of the Virasoro algebra of central charge c = c() 1. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure.
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