Title: Realization of functions on the symmetrized bidisc,
Abstract: We prove a realization formula and a model formula for analytic functions
with modulus bounded by $1$ on the symmetrized bidisc \[ G\stackrel{\rm def}{=}
\{(z+w,zw): |z|<1, \, |w| < 1\}. \] As an application we prove a Pick-type
theorem giving a criterion for the existence of such a function satisfying a
finite set of interpolation conditions.