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Part of the book series: NATO ASI Series ((ASIC,volume 440))

Abstract

The last few years have been good for the knowledge of Coxeter groups: the conjugacy problem has been solved, Coxeter groups have been shown to be automatic, and the structure of subgroups has been further exploited. In these notes, we survey some of these results, thus providing a sequel to three earlier ASI lectures on Coxeter groups.

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References

  • Alonso J.M., and Bridson M.R. [1993], “Semihyperbolic groups”, preprint Princeton University

    Google Scholar 

  • Bourbaki N. [1968], Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris

    MATH  Google Scholar 

  • Bridson M.R. [1991], “Geodesies and curvature in metric simplicial complexes”, in Group theory from a geometrical viewpoint, Ghys et al., ed., World Scientific, Singapore

    Google Scholar 

  • Brink B., and Howlett R. [1993], “A finiteness property and an automatic structure for Coxeter groups”, Math. Ann. 296, 179–190

    Article  MathSciNet  MATH  Google Scholar 

  • du Cloux F. [1990], “Un algorithme de forme normale pour les groupes de Coxeter”, Report Ecole Polytechnique, Palaiseau

    Google Scholar 

  • Cohen A.M. [1991], “Coxeter Groups and three Related Topics”, in Generators and Relations in Groups and Geometries, Castelvecchio Pascoli, Italy (April 1990) A. Barlotti, E.W. Ellers, P. Plaumann, and K. Strambach, eds., NATO ASI Series C: Matn. and Phys. Sciences #333, Kluwer Acad. Publ., Dordrecht, 235–278

    Google Scholar 

  • Davis M.W. [1983], “Groups generated by reflections and aspherical manifolds not covered by Eulidean space”, Annals of Math. 117, 293–324

    Article  Google Scholar 

  • Deodhar V. [1982], “On the root system of a Coxeter group”, Comm. Algebra 10, 611–630

    Article  MathSciNet  MATH  Google Scholar 

  • Dyer M [1990], “Relection Subgroups of Coxeter Systems”, Journal of Algebra 135, 57–73

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein D.B., Cannon J.W., Holt D.F., Levy S.V.F. Paterson M.S. and Thurston W.P. [1992], “Word Processing in Groups”, Jones and Bartlett, Boston

    MATH  Google Scholar 

  • Geck M., and Pfeiffer G. [1992], “On the Irreducible Characters of Hecke Algebras”, preprint, RWTH, Aachen

    Google Scholar 

  • Gersten S.M and Short H.B. [1990], “Inventiones Mathematicae”, 102 (1990), 305–334

    Article  MathSciNet  MATH  Google Scholar 

  • Gromov M. [1987], “Hyperbolic groups”, in Essays in Group Theory, S.M. Gersten, ed., MSRI series, No. 8, Springer-Verlag.

    Google Scholar 

  • Hermiller S. [1992], “Rewriting Systems for Coxeter groups”, preprint, Cornell University, May

    Google Scholar 

  • Humphreys J.E. [1990], Reflection groups and Coxeter groups, Cambridge University Press, Cambridge, UK.

    Book  MATH  Google Scholar 

  • Krammer D. [1993], “The Moussong complex and the conjugacy problem for Coxeter groups”, Preliminary notes, Univ. of Utrecht

    Google Scholar 

  • Le-Chenadec P. [1986], Canonical forms in finitely presented algebras, Pitman, London

    MATH  Google Scholar 

  • van Leeuwen M.A.A., Cohen A.M., and Lisser B. [1992], LiE, A package for Lie group computations #ISBN 90-74116-02-7, CAN, Amsterdam

    Google Scholar 

  • Milnor J. [1968], “A note on the curvature and fundamental group”, J. Diff. Geom. 2, 1–7

    MathSciNet  MATH  Google Scholar 

  • Monson B. [1987], “A family of uniform polytopes with symmetric shadows”, Geom. Dedicata 23, 355–363

    Article  MathSciNet  MATH  Google Scholar 

  • Moody R.V., and Patera J. [1992], “Quasicrystals and Icosians”, J. Physics A: Math. Gen. 26, 2829–2853

    Article  MathSciNet  Google Scholar 

  • Moussong G. [1988], “Hyperbolic Coxeter groups”, Ph.D. thesis, Ohio State University

    Google Scholar 

  • Mühlherr B. [1993], “Coxeter groups in Coxeter groups”, preprint, Math. Univ. Tübingen

    Google Scholar 

  • Pasqualucci R. [1992], “The conjugacy classes in the Weyl groups”, Math. Degree Thesis, La Sapienza University, Roma

    Google Scholar 

  • Scharlau R. [1993], “Buildings”, preprint 93-016, to appear in Handbook of incidence geometry, ed. F. Buekenhout, Bielefeld

    Google Scholar 

  • Scherbak O.P. [1988], “Wavefronts and reflection groups”, Russ. Math. Surveys 43, 149–194

    Article  Google Scholar 

  • Tits J. [1981], “A local approach to buildings”, in The Geometric Vein (the Coxeter Festschrift), C. Davis, B. Griinbaum and F.A. Sherk, eds., Spring-Verlag, Berlin, 519–547

    Google Scholar 

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Cohen, A.M. (1994). Recent Results on Coxeter Groups. In: Bisztriczky, T., McMullen, P., Schneider, R., Weiss, A.I. (eds) Polytopes: Abstract, Convex and Computational. NATO ASI Series, vol 440. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0924-6_1

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  • DOI: https://doi.org/10.1007/978-94-011-0924-6_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4398-4

  • Online ISBN: 978-94-011-0924-6

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