Abstract
In this article we study quotients of deformations of simple singularities, and attempt to characterise them using subsystems of simple root systems. The quotient of a semiuniversal deformation of a simple singularity of inhomogeneous type Br (r≥2), Cr (r≥3), F4 or G2 by the natural symmetry of the associated Dynkin diagram is a deformation of a simple singularity of homogeneous type X=Ds, E6 or E7, but not semiuniversal anymore. Therefore not all subdiagrams of X appear as singular configurations of the fibres of the deformation. We propose a conjecture for the types of singular configurations in terms of sub-root systems of a root system of type X and prove it for types B2,B3,C3,F4 and G2.
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