  Irreducible sigma models, i.e. those for which the partition function does
not factorise, are defined on Riemannian spaces with irreducible holonomy
groups. These special geometries are characterised by the existence of
covariantly constant forms which in turn give rise to symmetries of the
supersymmetric sigma model actions. The Poisson bracket algebra of the
corresponding currents is a W-algebra. Extended supersymmetries arise as
special cases.
