The word and riemannian metrics on lattices of semisimple groups
Lubotsky, Alexander ; Mozes, Shahar ; Raghunathan, Madabusi S.
Publications Mathématiques de l'IHÉS, Tome 92 (2000), p. 5-53 / Harvested from Numdam
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Publié le : 2000-01-01
@article{PMIHES_2000__91__5_0,
     author = {Lubotsky, Alexander and Mozes, Shahar and Raghunathan, Madabusi S.},
     title = {The word and riemannian metrics on lattices of semisimple groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {92},
     year = {2000},
     pages = {5-53},
     zbl = {0988.22007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_2000__91__5_0}
}

Lubotsky, Alexander; Mozes, Shahar; Raghunathan, Madabusi S. The word and riemannian metrics on lattices of semisimple groups. Publications Mathématiques de l'IHÉS, Tome 92 (2000) pp. 5-53. http://gdmltest.u-ga.fr/item/PMIHES_2000__91__5_0/

[Be] H. Behr, Endliche Erzangbarkeit arithmetischer Gruppen über Functionenkörpern, Invent. Math. 7 (1969), 1-32. | MR 39 #213 | Zbl 0169.34802

[Bo] A. Borel, Introduction aux Groupes arithmétiques, Hermann, 1969. | MR 39 #5577 | Zbl 0186.33202

[BT1] A. Borel, J. Tits, Groupes réductifs, Publ. Math. IHES, 27 (1965), 55-110. | Numdam | MR 34 #7527 | Zbl 0145.17402

[BT2] A. Borel, J. Tits, Éléments unipotents et sous-groupes paraboliques de groupes réductifs, Invent. Math. 12 (1971), 95-104. | MR 45 #3419 | Zbl 0238.20055

[GR] H. Garland and M. S. Raghunathan, Fundamental domains for lattices in R-rank one semisimple Lie groups, Ann. of Math., 92 (1970), 279-326. | MR 42 #1943 | Zbl 0206.03603

[Gr1] M. Gromov, Hyperbolic groups, 8 (1980), Springer-Verlag, in “Essays in Group Theory”, Ed. S. M. Gersten, M.S.R.I. series. | MR 89e:20070 | Zbl 0634.20015

[Gr2] M. Gromov, Asymptotic invariants of infinite groups, Geometric Group Theory, Proceedings of the symposium held in Sussex, July 1991, vol. 2. Eds. G. A. Niblo and M. A. Roller. LMS, Lecture Notes series 182, Cambridge University Press, 1993. | Zbl 0841.20039

[Ha1] G. Harder, Minkowskische Reductions Theorie über Functionenkörpern, Invent. Math. 7 (1969), 33-54. | MR 44 #1667 | Zbl 0242.20046

[Ha2] G. Harder, Über die Galoiskohomologie halbeinfacher algebraicher Gruppen, III, J. Reine Angew. Math. 274/275 (1975), 125-138. | MR 52 #3352 | Zbl 0317.14025

[Ja] G. J. Janusz, Algebraic Number Fields, Academic Press, 1973. | MR 51 #3110 | Zbl 0307.12001

[Kn] M. Kneser, Schwache Approximation in Algebraische Gruppen, Colloque sur la théorie de groupes algébriques, Bruxelles, Louvain, Paris (1962), 41-52. | Zbl 0171.29102

[Ko] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. 74 (1961), 329-386. | MR 26 #265 | Zbl 0134.03501

[Lu] A. Lubotzky, Lattices in rank one Lie groups over local fields, Geometric and Functional Analysis 1 (1991), 405-431. | MR 92k:22019 | Zbl 0786.22017

[LMR] A. Lubotzky, S. Mozes and M. S. Raghunathan, Cyclic subgroups of exponential growth and metrics on discrete groups, C. R. Acad. Sci. Paris, Série I, 317 (1993), 735-740. | MR 94m:22009 | Zbl 0786.22016

[Ma] G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, 1990. | Zbl 0732.22008

[PR] V. Platonov, A. Rapinchuk, Algebraic Groups and Number Theory, New York, Academic Press, 1994. | MR 95b:11039 | Zbl 0841.20046

[Ra1] M. S. Raghunathan, Discrete Subgroups of Lie Groups, Springer-Verlag, 1968.

[Ra2] M. S. Raghunathan, Discrete subgroups of algebraic groups over local fields of positive characteristics, Proc. Indian Acad. Sci. (Math. Sci.) 99 (1989), 127-146. | MR 91a:22010 | Zbl 0689.22004

[Se] J.-P. Serre, Trees, Springer-Verlag, 1980. | MR 82c:20083 | Zbl 0548.20018

[St] R. Steinberg, Lectures on Chevalley Groups, Yale University, 1968. | MR 57 #6215

[Th] W. P. Thurston, Groups, tilings and finite state automata, Lecture notes, AMS colloquium lectures (1990).

[Ti1] J. Tits, Free subgroups in linear groups, J. of Algebra 20 (1972), 250-270. | MR 44 #4105 | Zbl 0236.20032

[Ti2] J. Tits, Classification of Algebraic Simple Groups, Algebraic Groups and Discontinuous Groups, Proc. Symp. Pure Math. No 9, AMS Providence (1966). | Zbl 0238.20052

[Ve] T.N. Venkataramana, On super-rigidity and arithmeticity of lattices in semisimple groups, Invent. Math. 92 (1988), 255-306. | MR 89c:20073 | Zbl 0649.22008