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This article is cited in 11 scientific papers (total in 11 papers)
Unitary reflection groups associated with singularities of functions with cyclic symmetry
V. V. Goryunov University of Liverpool
Abstract:
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.
Received: 29.04.1999
Citation:
V. V. Goryunov, “Unitary reflection groups associated with singularities of functions with cyclic symmetry”, Uspekhi Mat. Nauk, 54:5(329) (1999), 3–24; Russian Math. Surveys, 54:5 (1999), 873–893
Linking options:
https://www.mathnet.ru/eng/rm202https://doi.org/10.1070/rm1999v054n05ABEH000202 https://www.mathnet.ru/eng/rm/v54/i5/p3
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Abstract page: | 557 | Russian version PDF: | 215 | English version PDF: | 28 | References: | 72 | First page: | 2 |
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