  Anomalous surface abundances are observed in a fraction of the low-mass stars
of Galactic globular clusters, that may originate from hot-hydrogen-burning
products ejected by a previous generation of massive stars. We present and
investigate a scenario in which the second generation of polluted low-mass
stars can form in shells around cool supergiant stars within a young globular
cluster. Simulations of low-Z massive stars (M$_{\rm i}\sim$ 150$-$600
M$_{\odot}$) show that both core-hydrogen-burning cool supergiants and hot
ionizing stellar sources are expected to be present simulaneously in young
globular clusters. Under these conditions, photoionization-confined shells form
around the supergiants. We find that the shell is gravitationally unstable on a
timescale that is shorter than the lifetime of the supergiant, and the
Bonnor-Ebert mass of the overdense regions is low enough to allow star
formation. Since the low-mass stellar generation formed in this shell is made
up of the material lost from the supergiant, its composition necessarily
reflects the composition of the supergiant wind. We show that the wind contains
hot-hydrogen-burning products, and that the shell-stars therefore have very
similar abundance anomalies that are observed in the second generation stars of
globular clusters. Considering the mass-budget required for the second
generation star-formation, we offer two solutions. Either a top-heavy initial
mass function is needed with an index of $-$1.71..$-$2.07. Alternatively, we
suggest the shell-stars to have a truncated mass distribution, and solve the
mass budget problem by justifiably accounting for only a fraction of the first
generation. Even without forming a photoionizaton-confined shell, the cool
supergiant stars predicted at low-Z could contribute to the pollution of the
interstellar medium of the cluster from which the second generation was born.
