On stratifying pairs of linear mappings
Christopher G. Gibson, T. D. Ward · Pacific Journal of Mathematics · 1982
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 A v , D n , E 6 , E Ίi E 8 such stratifications are provided by the orbits; and for thQ extended Dynkin diagrams A n , D n , E 6 , E 7 , E 8 one might expect to obtain such stratifications by 'neglecting moduli', in an obvious way.This is known to be the case for A o .For A t we show that this procedure does yield a stratification, and that at least the regular strata satisfy the Whitney conditions.