Presentations for crystallographic complex reflection groups

DOI10.1007/BF02549209zbMath0889.20028OpenAlexW2016342108MaRDI QIDQ1377340

Gunter Malle

Publication date: 23 June 1998

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02549209

zbMATH Keywords

presentationsaffine Weyl groupsfundamental groupsDynkin diagramsirreducible crystallographic complex reflection groupsspaces of regular orbits

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Other geometric groups, including crystallographic groups (20H15) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Reflection groups, reflection geometries (51F15)

Related Items

Symmetric \(X _{9}\) singularities and complex affine reflection groups, Automorphisms of \(P_8\) singularities and the complex crystallographic groups, Steinberg's fixed point theorem for crystallographic complex reflection groups, Steinberg's theorem for crystallographic complex reflection groups, On elliptic Calogero-Moser systems for complex crystallographic reflection groups, Reflection Groups, Generalized nil-Coxeter algebras over discrete complex reflection groups, Extended root graphs for complex reflection groups

Uses Software

• GAP
• kbmag

Cites Work

• The fundamental groups of the spaces of regular orbits of the affine Weyl groups
• Complex reflection groups
• Finite complex reflection groups
• Finite Unitary Reflection Groups
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