The conjugacy problem for Coxeter groups

Groups, Geometry, and Dynamics

Volumn 3, Issue 1, 2009, Pages 71-171

  Krammer, Daan ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Conjugacy problem; Coxeter group; Parabolic closure; Tits cone

Indexed keywords

EID: 67650886262     PISSN: 16617207     EISSN: 16617215     Source Type: Journal    
DOI: 10.4171/GGD/52     Document Type: Article

References (50)

1. J. M. Alonso et al., Notes on word hyperbolic groups (ed. by H. Short). In Group theory from a geometrical viewpoint (Trieste, 1990), World Scientific, Singapore 1991, 3-63. Zbl 0849.20023 MR 1170363
2. U. Baumgartner, Totally disconnected, locally compact groups as geometric objects. A survey of work in progress. In Geometric group theory (Geneva and Barcelona, 2005). Trends Math., Birkhäuser Verlag, Basel 2007, 1-20. Zbl 05343228 MR 2395785
3. U. Baumgartner, B. Rémy, and G. A. Willis, Flat rank of automorphism groups of buildings. Transform. Groups 12 (2007), 413-436. Zbl 1145.22012 MR 2356316
4. A. F. Beardon, The geometry of discrete groups. Grad. Texts in Math. 91, Springer-Verlag, New York 1983. Zbl 0528.30001 MR 0698777
5. R. Benedetti and C. Petronio, Lectures on hyperbolic geometry. Universitext, Springer-Verlag, Berlin 1992. Zbl 0768.51018 MR 1219310
6. A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences. Academic Press, New York 1979. Zbl 0484.15016 MR 0544666
7. A. Björner and F. Brenti, Combinatorics of Coxeter groups. Grad. Texts in Math. 231, Springer-Verlag, New York 2005. Zbl 1110.05001 MR 2133266
8. N. Bourbaki, Groupes et algèbres de Lie, Ch. 4-6. Hermann, Paris 1968; Masson, Paris 1981. Zbl 0186.33001 MR 0240238
9. M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature. Grundlehren Math. Wiss. 319, Springer-Verlag, Berlin 1999. Zbl 0988.53001 MR 1744486
10. B. Brink and R. B. Howlett, A finiteness property and an automatic structure for Coxeter groups. Math. Ann. 296 (1993), 179-190. Zbl 0793.20036 MR 1213378
11. A. Brønsted, An introduction to convex polytopes. Grad. Texts in Math. 90, Springer-Verlag, New York 1983. Zbl 0509.52001 MR 0683612
12. K. S. Brown, Buildings. Springer Monogr. Math., Springer-Verlag, New York 1998. Zbl 0922.20034 MR 1644630
13. P.-E. Caprace, Conjugacy of one-ended subgroups of Coxeter groups and parallel walls. Preprint 2005. arXiv:math/0508057
14. P.-E. Caprace, Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls. Algebr. Geom. Topol. 6 (2006), 1987-2029. Zbl 05118585 MR 2263057
15. P.-E. Caprace, Buildings with isolated subspaces and relatively hyperbolic Coxeter groups. Preprint 2007. arXiv:math/0703799
16. P.-E. Caprace and F. Haglund, On geometric flats in the CAT (0) realization of Coxeter groups and Tits buildings. Canad. J. Math., to appear; Preprint 2006. arXiv:math/0607741
17. P.-E. Caprace and B. Mühlherr, Reflection triangles in Coxeter groups and biautomaticity. J. Group Theory 8 (2005), 467-489. Zbl 1081.20049 MR 2152693
18. P.-E. Caprace and B. Rémy, Simplicity and supperrigidity of twin building lattices. Invent. Math., to appear; Preprint 2006. arXiv:math/0607664
19. A. M. Cohen, Coxeter groups and three related topics. In Generators and relations in groups and geometries, Castelvecchio Pascoli (Lucca), 1990, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 333, Kluwer Acad. Publ., Dordrecht 1991, 235-278. Zbl 0742.20040 MR 1206917
20. A. M. Cohen, Recent results on Coxeter groups. In Polytopes: abstract, convex and computational (Scarborough, Ontario, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 440, Kluwer Acad. Publ., Dordrecht 1994, 1-19. Zbl 0830.20060 MR 1322055
21. G. E. Collins and R. Loos, Real zeros of polynomials. In Computer algebra: symbolic and algebraic computation, Springer-Verlag, Vienna 1983, 83-94. Zbl 0533.68038 MR 0728967
22. M. Coornaert, T. Delzant, and A. Papadopoulos, Géométrie et théorie des groupes. Lecture Notes in Math. 1441, Springer-Verlag, Berlin 1990 Zbl 0727.20018 MR 1075994
23. ij=1. J. London Math. Soc. 10 (1935) 21-25. JFM 61.0097.05 Zbl 0010.34202
24. J. H. Davenport, Y. Siret, and E. Tournier, Computer algebra. Academic Press, London 1988. Zbl 0679.68058 MR 0975254
25. M. W. Davis, The geometry and topology of Coxeter groups. London Math. Soc. Monogr. 32, Princeton University Press, Princeton, NJ, 2007. Zbl 1142.20020 MR 2360474
26. M. Dehn, über unendliche diskontinuierliche Gruppen. Math. Ann. 71 (1912), 116-144. JFM 42.0508.03
27. V. V. Deodhar, On the root system of a Coxeter group. Comm. Algebra 10 (1982), 611-630. Zbl 0491.20032 MR 647210
28. V. V. Deodhar, A note on subgroups generated by reflections in Coxeter groups. Arch. Math. (Basel) 53 (1989), 543-546. Zbl 0688.20028 MR 1023969
29. S. van Dongen, Exact computation of the sign of a real algebraic number. Master's thesis, Technical University of Eindhoven, Eindhoven 1994.
30. M. Dyer, Reflection subgroups of Coxeter systems. J. Algebra 135 (1990), 57-73. Zbl 0712.20026 MR 1076077
31. D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, and W. P. Thurston, Word processing in groups. Jones and Bartlett Publishers, Boston 1992. Zbl 0764.20017 MR 1161694
32. D. Epstein and D. Holt, The linearity of the conjugacy problem in word-hyperbolic groups. Internat. J. Algebra Comput. 16 (2006), 287-305. Zbl 1141.20028 MR 2228514
33. P. de la Harpe, An invitation to Coxeter groups. In Group theory from a geometrical viewpoint (Trieste, 1990), World Scientific, Singapore 1991, 193-253. Zbl 0840.20033 MR 1170367
34. D. F. Holt, B. Eick, and E. A. O'Brien, Handbook of computational group theory. Chapman & Hall/CRC Press, Boca Raton 2005. Zbl 1091.20001 MR 2129747
35. R. B. Howlett, Normalizers of parabolic subgroups of reflection groups. J. London Math. Soc. (2) 21 (1980), 62-80. Zbl 0427.20040 MR 576184
36. J. E. Humphreys, Reflection groups and Coxeter groups. Cambridge Stud. Adv. Math. 29, Cambridge University Press, Cambridge 1990. Zbl 0725.20028 MR 1066460
37. R. D. Hurwitz, A survey of the conjugacy problem. In Contributions to group theory, Contemp. Math. 33, Amer. Math. Soc., Providence, RI, 1984, 278-298. Zbl 0549.20023 MR 0767116
38. N. Jacobson, Lectures in abstract algebra. III. Grad. Texts in Math. 32, Springer-Verlag, New York 1975. Zbl 0322.12001 MR 0392906
39. D. E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Zbl 0477.65002 MR 0633878
40. Yu. I. Manin, A course in mathematical logic. Grad. Texts in Math. 53, Springer-Verlag, New York 1977. Zbl 0383.03002 MR 0457126
41. G. Maxwell, Sphere packings and hyperbolic reflection groups. J. Algebra 79 (1982), 78-97. Zbl 0556.51003 MR 679972
42. J. Milnor, A note on curvature and fundamental group. J. Differential Geometry 2 (1968), 1-7. Zbl 0162.25401 MR 0232311
43. G. Moussong, Hyperbolic Coxeter groups. Ph. D. thesis, The Ohio State University, Columbus 1988. http://www.ohiolink.edu/etd/view.cgi?osu1114437114
44. L. Paris, Irreducible Coxeter groups. Internat. J. Algebra Comput. 17 (2007), 427-447. Zbl 1134.20046 MR 2333366
45. L. Solomon, A Mackey formula in the group ring of a Coxeter group. J. Algebra 41 (1976), 255-264. Zbl 0355.20007 MR 0444756
46. J. Tits, Le problème des mots dans les groupes de Coxeter. In Symposia Mathematica, vol. 1, Teoria dei gruppi, INDAM, Roma, 13-16 dicembre 1967, Academic Press, London 1969, 175-185. Zbl 0206.03002 MR 0254129
47. È. B. Vinberg, Discrete linear groups that are generated by reflections. Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1072-1112
48. English transl. Math. USSR-Izv. 5 (1971), 1083-1119. Zbl 0247.20054 MR 0302779
49. È. B. Vinberg, Hyperbolic groups of reflections. Uspekhi Mat. Nauk 40 (1985), 29-66
50. English transl. Russian Math. Surveys 40 (1985), 31-75. Zbl 0579.51015 MR 783604