Symmetries of unimodal singularities and complex hyperbolic reflection groups



Haddley, Joel A
Symmetries of unimodal singularities and complex hyperbolic reflection groups. [Unspecified]

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Abstract

In search of discrete complex hyperbolic reflection groups in a singularity context, we consider cyclic symmetries of the 14 exceptional unimodal function singularities. In the 3-variable case, we classify all the symmetries for which the restriction of the intersection form of an invariant Milnor fibre to a character subspace has positive signature 1, and hence the corresponding equivariant monodromy is a reflection subgroup of U(k − 1,1). For such subspaces, we construct distinguished vanishing bases and their Dynkin diagrams. For k = 2, the projectivised hyperbolic monodromy is a triangle group of the Poincaré disk. For k = 3, we identify some of the projectivised monodromy groups within a recently published survey by J. R. Parker.

Item Type: Unspecified
Additional Information: Date: 2011-06 (completed)
Subjects: Q Science > QA Mathematics
Divisions: ?? dep_math ??
Depositing User: Symplectic Admin
Date Deposited: 30 Nov 2011 17:04
Last Modified: 09 Jan 2021 08:57
URI: https://livrepository.liverpool.ac.uk/id/eprint/3313