Geodesic
Unitary reflection groups associated with singularities of functions with cyclic symmetry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 54 (1999) no. 5, pp. 873-893

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Finite groups generated by Euclidean reflections have been commonplace in various problems of singularity theory since their relationship with the classification of critical points of functions was discovered by Arnol'd [1], [2]. We show that a number of finite groups generated by unitary reflections are also naturally related to singularities of functions, namely, those invariant under a unitary reflection of finite order. To this end, we consider germs of functions on a manifold with boundary and lift them to a cyclic covering of the manifold, ramified over the boundary. This construction provides a new notion of roots for the groups under consideration and provides skew-Hermitian analogues of these groups. 
@article{RM_1999_54_5_a0,
     author = {V. V. Goryunov},
     title = {Unitary reflection groups associated with singularities of functions with cyclic symmetry},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {873--893},
     publisher = {mathdoc},
     volume = {54},
     number = {5},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1999_54_5_a0/}
}
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V. V. Goryunov. Unitary reflection groups associated with singularities of functions with cyclic symmetry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 54 (1999) no. 5, pp. 873-893. http://geodesic.mathdoc.fr/item/RM_1999_54_5_a0/