We show how to relate Schramm-Loewner Evolutions (SLE) to highestweight representations of infinite-dimensional Lie algebras that are singular at level two, using the conformal restriction properties studied by Lawler, Schramm and Werner in [33]. This confirms the prediction from conformal field theory that two-dimensional critical systems are related to degenerate representations.

The unitarizable modules in the analytic continuation of the holomorphic discrete series for tube type domains are realized as Hilbert spaces obtained through the Laplace transform.