The complex linear
representations (of fixed dimension) of an oriented graph form a finite dimensional
vector space M with a natural action of a product G of general linear groups. It is
interesting to look for natural Whitney stratifications of M invariant under G. For
the Dynkin diagrams An, Dn, E6, E7, E8 such stratifications are provided by the
orbits; and for the extended Dynkin diagrams Ãn, Dn, Ẽ6, Ẽ7, Ẽ8 one might
expect to obtain such stratifications by ‘neglecting moduli’, in an obvious way. This is
known to be the case for Ã0. For Ã1 we show that this procedure does yield
a stratification, and that at least the regular strata satisfy the Whitney
conditions.
