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Fundamental Domains for Finite Subgroups in U(2) and Configurations of Lagrangians

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Abstract

We show that every finite subgroup of U(2) is contained with index two in a group generated by involutions fixing Lagrangian planes. We describe fundamental domains for their action on \({\mathbb C}^{2}\) related to the configuration of these Lagrangian planes.

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References

  1. Conway, J. H. and Smith, D. A.: On Quaternions and Octonions. K. Peters. 2003.

  2. H.S.M. Coxeter (1991) Regular Complex Polytopes Cambridge University Press Cambridge

    Google Scholar 

  3. P. Du Val (1964) Homographies, Quaternions and Rotations, Oxford Mathematical Monographs Science Publishers Oxford

    Google Scholar 

  4. E. Falbel (2001) ArticleTitleFinite groups generated by involutions on Lagrangian planes of C2 Canad. Math. Bull 44 IssueID4 408–419

    Google Scholar 

  5. Falbel, E., Marco, J.-P. and Scha.hauser, F.: Classifying triples of Lagrangians in a Hermitian vector space. Topology and its Applications. To appear.

  6. E. Falbel V. Zocca (1999) ArticleTitleA Poincarë’s polyhedron theorem for complex hyperbolic geometry J. Reine Angew. Math 516 138–158

    Google Scholar 

  7. Goldman, W.: Complex Hyperbolic Geometry, Oxford Mathematical Monographs, Oxford Science Publications, 1999.

  8. D. Mostow G. (1980) ArticleTitleOn a remarkable class of polyhedra in complex hyperbolic space Paci.c J. Math 86 171–276

    Google Scholar 

  9. A.J. Nicas (1991) ArticleTitleClassifying pairs of Lagrangians in a hermitean vector space Topology and its Applications 42 71–81 Occurrence Handle10.1016/0166-8641(91)90033-I

    Article  Google Scholar 

  10. Paupert, J.: Thesis, Universite’ Paris 6, to appear.

  11. Schwartz, R. E.: Complex hyperbolic triangle groups. In: Proceedings of the International Congress of Mathematicians, 1 (2002) 339–350.

  12. G.C. Shephard J.A. Todd (1954) ArticleTitleFinite unitary reflection groups Canad. J. Math 6 274–304

    Google Scholar 

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Authors and Affiliations

  1. Institut de Mathématiques, Université Pierre et Marie Curie, 4 place Jussieu, F-75252, Paris

    Elisha Falbel & Julien Paupert

Authors
  1. Elisha Falbel
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  2. Julien Paupert
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Correspondence to Elisha Falbel.

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Falbel, E., Paupert, J. Fundamental Domains for Finite Subgroups in U(2) and Configurations of Lagrangians. Geom Dedicata 109, 221–238 (2004). https://doi.org/10.1007/s10711-004-2455-2

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  • DOI: https://doi.org/10.1007/s10711-004-2455-2

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