Conformal restriction, highest-weight representations and SLE

Roland Friedrich, Wendelin Werner

Published 2003-01-14, updated 2003-05-28Version 3

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.