Rigidity of commensurators and irreducible lattices

Inventiones Mathematicae

Volumn 141, Issue 1, 2000, Pages 1-54

  Shalom, Yehuda ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349067     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220000064     Document Type: Article

References (50)

1. [Ad] S. Adams, Reduction of cocycles with hyperbolic targets, Ergodic Theory and Dynamical Systems 16 (1996), 1111-1145
2. [BaLu] H. Bass, A. Lubotzky, Tree lattices, Birkhauser, Forthcoming
3. [Be] M. Bekka, On uniqueness of invariant means, Proc. of the AMS 126 (1998), 507-514
4. [BeK] I.N. Bernstein, D.A. Kazhdan, The one dimensional cohomology of discrete subgroups, Func. Anal. Appl. 4 (1970), 1-4
5. [BeLo] M. Bekka, N. Louvet, On a variant of Kazhdan's property (T) for subgroups of semisimple groups, Ann. Inst. Fourier (Grenoble) 47 (1997), 1065-1078
6. [BG] N. Benakli, Y. Glasner, Automorphism groups of trees acting locally with affine permutations, preprint
7. [BK] H. Bass, R. Kulkarni, Uniform tree lattices, J. of AMS 3 (1990), 843-902
8. [BM1] M. Burger, S. Mozes, CAT(-1) spaces, divergence groups and their commensurators, J. of AMS 9 (1996), 57-93
9. [BM2] M. Burger, S. Mozes, Finitely presented simple groups and products of trees, C.R. Acad. Sci. Ser. I 324 no.7 (1997), 747-752
10. [BM3] M. Burger, S. Mozes, Lattices in products of trees, preprint
11. [BM4] M. Burger, S. Mozes, Groups acting on trees: from local to global structures, preprint
12. [BMZ] M. Burger, S. Mozes, R.J. Zimmer, Linear representations and arithmrticity for lattices in products of trees, in preparation
13. [Bou] M. Bourdon, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, GAFA (7) (1997), 245-268
14. [Bur] M. Burger, Rigidity properties of group actions on CAT(0) spaces, Proc. of the ICM (Zurich 1994), Birkhauser (1995), 761-769
15. [BuSa] M. Burger, P. Sarnak, Ramanujan duals II, Invent. math. 106 (1991), 1-11
16. [BW] A. Borel, N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies, Princeton Univ. Press, 1980
17. [Ca] L. Carbone, Nonuniform lattices in uniform trees, submitted
18. [CG] L. Carbone, H. Garland, Lattices in Kac-Moody groups, Math. Res. Letters, to appear
19. [Cl] J.A. Clarkson, Uniformly convex spaces, Trans. of the AMS 40 (1936), 396-414
20. [De] P. Delorme, 1-cohomologie des représentations unitaires des groupes de Lie semi-simple et résolubles. Produits tensoriels continus et représentations, Bull. Soc. Math. France 105 (1977), 289-323
21. [Gao] Y. Gao, Superrigidity for homomorphisms into isometry groups of CAT(-1) spaces, Transformation Groups 3 (1997), 289-323
22. [Gu] A. Guichardet, Cohomologic des groups topologies et des algèbres de Lie, Cedic-F Nathan 1980
23. [Ha] F. Haglund, Réseaux de Coxeter-Davis et commensurateurs, Ann. Inst. Four. 48 (1998), 649-666
24. [HP] F. Haglund, F. Paulin, Simplicité de groupes d'automorphismes d'espace à courbure négative, preprint
25. [HPV] F. Haglund, F. Paulin, A. Valette, Coxeter groups virtually act on product of trees, in preparation
26. [HV] P. de la Harpe, A. Valette, La Propriété (T) de Kazhdan pour les groupes localement compacts, Asterisque 175, Société Math. de France 1989
27. [Liu] Y.S. Liu, Density of the commensurability group of uniform tree lattices 165, J. of Algebra (1994), 346-359
28. [LMR] A. Lubotzky, S. Mozes, M.S. Raghunathan, Cyclic subgroups of exponential growth and metrics on discrete groups, C.R. Acad. Sci. Paris Ser. I 317 (1993), 735-740
29. [LMZ] A. Lubotzky, S. Mozes, R. Zimmer, Superrigidity for the commensurability group of tree lattices, Comment. Math. Helv. 69 (1994), 523-548
30. [Lo] N. Louvet, Cohomological rigidity for lattices in products of groups, C. R. Acad. Sci. Paris 327, Ser. I (1998), 133-138
31. [Mar1] G.A. Margulis, Discrete subgroups of semisimple groups, Springer, Berlin, 1991
32. [Mar2] G.A. Margulis, On the decomposition of discrete subgroups into amalgams, Selecta Mathematics Sovietica 1 (1981), 197-213
33. [Mar3] G.A. Margulis, Finiteness of quotient groups of discrete subgroups, Func. Anal. Appl. 13 (1979), 178-187
34. [Mar4] G.A. Margulis, Superrigidity for commensurability subgroups and generalized harmonic maps, unpublished manuscript (1994)
35. [Moz] S. Mozes, Product of trees, lattices and simple groups, Proceedings of the ICM (Berlin 1998) - Doc. Math. (1998), 571-582
36. [Pa] P. Pansu, Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles, Bull. Soc. Math. France 126, no. 1 (1998), 107-139
37. [Pi] R. Pink, Compact subgroups of linear algebraic groups, J. Algebra 206 (1998), 438-504
38. [Re] B. Remy, Construction de réseaux en théorie de Kac-Moody, preprint (1999)
39. [Sch] K. Schmidt, Amenability, Kazhdan's property (T), strong ergodicity and invariant means for ergodic group actions, Ergodic Theory and Dynamical Systems 1 (1981), 223-236
40. [Sh1] Y. Shalom, Rigidity and cohomology of unitary representations, IMRN 16 (1998), 829-849
41. [Sh2] Y. Shalom, Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group, preprint
42. [Sh3] Y. Shalom, Explicit Kazhdan constants for representations of semisimple and arithmetic groups, preprint
43. [Sh4] Y. Shalom, Quasi-isometric amenable groups and uniform measure equivalence, in preparation
44. [Ti1] J. Tits, Sur le groupe des automorphismes d'un arbre, in: Essays on Topology and Related Topics pp. 188-211, Springer, New York 1970
45. [Ti2] J. Tits, Uniqueness and presentation of Kac-Moody groups over fields, J. of Algebra 105 (1987), 542-573
46. [Va] A. Valette, Old and new about Kazhdan's property (T), in: Representations of Lie groups and quantum groups (Trento, 1993), 271-333, Pitman Res. Notes Math. Ser. 311, 1994
47. [Ve] T.N. Venkataramana, On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic, Invent. math. 92 (1988), 255-306
48. [VK] A.M. Vershik, S.I. Karpushev, Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions, Math. USSR Sbor 119 (1982), 521-533
49. [Zi1] R.J. Zimmer, Ergodic theory and semisimple groups, Birkhäuser, 1985
50. [Zi2] R.J. Zimmer, Ergodic actions of semisimple groups and product relations, Ann. Math. 118 (1983), 9-19