  The most massive Galactic globular cluster, Omega centauri, appears to have
multiple populations. Its bluest main sequence and extended horizontal branch
stars are suggested to have the common origin, that is, an extremely high
helium abundance of Y ~ 0.4. The high helium abundance is most often attributed
to asymptotic giant branch (AGB) stars. In this study we test the AGB
hypothesis. We simulate the maximum-AGB models where the impact of AGB stars is
maximised by assuming that supernova explosions do not affect the chemical
evolution of the proto cloud. We compare the enrichment history of helium,
metals, carbon and nitrogen to the observed values. Even under the most
generous condition, the maximum-AGB models fail to reproduce the large values
of helium Y ~ 0.4 and helium enrichment parameter Delta Y / Delta Z ~ 70 which
were deduced from the colour-magnitude diagram fits. They also fail to
reproduce the C and N contents of the blue population spectroscopically
determined. We conclude that the AGB scenario with the canonical stellar
evolution theory cannot explain the observational constraints and that the self
chemical enrichment does not provide a viable solution. Alternative processes
are desperately called for.
