  We construct the restricted sine-Gordon theory by truncating the sine-Gordon
multi-soliton Hilbert space for the repulsive coupling constant due to the
quantum group symmetry $SL_q(2)$ which we identify from the Korepin's
$S$-matrices. We connect this restricted sine-Gordon theory with the minimal
($c<1$) conformal field theory ${\cal M}_{p/p+2}$ ($p$ odd) perturbed by the
least relevent primary field $\Phi_{1,3}$. The exact $S$-matrices are derived
for the particle spectrum of a kink and neutral particles. As a consistency
check, we compute the central charge of the restricted theory in the UV limit
using the thermodynamic Bethe ansatz analysis and show that it is equal to that
of ${\cal M}_{p/p+2}$.
