  We perform canonical quantization of the WZW model with defects and
permutation branes. We establish symplectomorphism between phase space of WZW
model with $N$ defects on cylinder and phase space of Chern-Simons theory on
annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model
with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$
Wilson lines. We obtained also symplectomorphism between phase space of the
$N$-fold product of the WZW model with boundary conditions specified by
permutation branes, and phase space of Chern-Simons theory on sphere with $N$
holes and two Wilson lines.
