Invariant Symmetries of Unimodal Function Singularities

We classify finite order symmetries $g$ of the 14 exceptional unimodal function singularities $f$ in 3 variables, which satisfy a so-called splitting condition. This means that the rank 2 positive subspace in the vanishing homology of $f$ should not be contained in one eigenspace of $g_\star$. We also obtain a description of the hyperbolic complex reflection groups appearing as equivariant monodromy groups acting on the hyperbolic eigensubspaces arising.