Conformal restriction, highest-weight representations and SLE

Abstract

We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite dimensional Lie Algebras using the conformal restriction properties studied by Lawler, Schramm and Werner in the paper arXiv:math.PR/0209343. This confirms the prediction from theoretical physics and conformal field theory that two-dimensional critical systems are related to such degenerate representations.

To appear in Comm. Math. Phys. These results were anounced in arXiv:math.PR/0209382

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