@article{PMIHES_1999__90__145_0, author = {Shalom, Yehuda}, title = {Bounded generation and {Kazhdan{\textquoteright}s} property $(T)$}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {145--168}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {90}, year = {1999}, mrnumber = {2001m:22030}, zbl = {0980.22017}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1999__90__145_0/} }
TY - JOUR AU - Shalom, Yehuda TI - Bounded generation and Kazhdan’s property $(T)$ JO - Publications Mathématiques de l'IHÉS PY - 1999 SP - 145 EP - 168 VL - 90 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1999__90__145_0/ LA - en ID - PMIHES_1999__90__145_0 ER -
Shalom, Yehuda. Bounded generation and Kazhdan’s property $(T)$. Publications Mathématiques de l'IHÉS, Tome 90 (1999), pp. 145-168. http://www.numdam.org/item/PMIHES_1999__90__145_0/
[AM] On bounded generation of SLn(Z), Inter. Jour. Alg. and Comp., Vol. 2, No. 4 (1992), 357-365. | MR | Zbl
and ,[BMS] Solution of the congruence subgroup problem for SLn (n ≥ 3) and Sp2n (n ≥ 2), IHES Publ., 33 (1967), 59-137. | Numdam | MR | Zbl
, and ,[Bur] Kazhdan constants for SL3(Z), J. Reine Angew. Math., 413 (1991), 36-67. | MR | Zbl
,[CK] Bounded elementary generation of SLn(O), Amer. J. Math., 105 (1983), 673-687. | MR | Zbl
and ,[CW] On the constructions of division chains in algebraic number fields, with applications to SL2, Comm Alg., 3 (1975), 481-524. | MR | Zbl
and ,[Di] Sur les fonctions continues p-adiques, Bull. Sci. Math. (2), 68 (1944), 79-95. | MR | Zbl
,[HRV] On the spectrum of the sum of generators for a finitely generated group, Israel J. of Math., 81 (1993), No. 1-2, 65-96. | MR | Zbl
, , ,[HV] La Propriété (T) de Kazhdan pour les Groupes Localement Compacts, Astérisque, 175, Société Math. de France (1989). | Numdam | Zbl
and ,[Is] Representations of Infinite-Dimensional Groups, Translations of Mathematical Monographs, 152, Amer. Math. Soc., Providence (1996). | MR | Zbl
,[Kal] SL3(C[x]) does not have bounded word length. Proceedings of the conference on Algebraic K-theory (Oberwolfach, 1980), Lecture Notes in Math., 966 (1982), 357-361. | MR | Zbl
,[Kaz] On a connection between the dual space of a group and the structure of its closed subgroups, Func. Anal. Appl. 1 (1967), 63-65. | Zbl
,[Lub1] Discrete Groups, Expanding Graphs and Invariant Measures, Birkhäuser, 1994. | MR | Zbl
,[Lub2] Subgroup growth and congruence subgroups, Invent. Math., 119 (1995), 267-295. | MR | Zbl
,[Mok] Harmonic forms with values in locally constant Hilbert bundles, Proceeding of the conference in honor of J. P. Kahane (Orsay 1993), J. Fourier Anal. Appl. (special issue), (1995), 433-453. | MR | Zbl
,[Mu] Bounded and finite generation of arithmetic groups, Canadian Mathematical Society Conference Proceedings, Vol. 15 (1995), 249-261. | MR | Zbl
,[MSY] Geometric superrigidity, Invent. Math., 113 (1993), 57-83. | MR | Zbl
, and ,[Pa] Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles, Bull. Soc. Math. France, 126 (1998), 107-139. | Numdam | MR | Zbl
,[PR] Abstract properties of S-arithmetic subgroups and the congruence subgroup problem, Izve. R. Acad. Sci. Ser. Math. (former Math. USSR Izvestiya), 56 (1992), 483-508. | Zbl
and ,[PS] Loop Groups, Oxford Mathematical Monographs, 1988. | Zbl
and ,[Rag] On the congruence subgroup problem, IHES Publ., 46 (1976), 107-161. | Numdam | MR | Zbl
,[Rap1] Congruence subgroup problem for algebraic groups: old and new, Astérisque, 209 (1992), 73-84. | MR | Zbl
,[Rap2] On the finite dimensional unitary representations of Kazhdan groups, Proc. of AMS, 127, No. 5 (1999), 1557-1562. | MR | Zbl
,[Rap3] On SS-rigid groups and A. Weil's criterion for local rigidity I, Manuscripta Math., 97 (1998), 529-543. | MR | Zbl
,[Sch] Ultra Calculus: An Introduction to p-Adic Analysis, Cambridge Studies in Advanced Mathematics 4, 1984. | MR | Zbl
,[Sh1] Explicit Kazhdan constants for representations of semisimple and arithmetic groups, Ann. Inst. Fourier (Grenoble), 50 (2000) No 3, 833-863. | Numdam | MR | Zbl
,[Sh2] Harmonic maps, superrigidity, and property (T), preprint.
,[Su] On the structure of the special linear group over polynomial rings, Math. USSR Izv., Vol. 11 (1977), 221-238. | Zbl
,[Tav] Bounded generation of Chevalley groups over rings of algebraic S-integers, Math. USSR Izv., 36 (1991), 101-128. | MR | Zbl
,[VGG] Representations of the group SL(2,R), where R is a ring of continuous functions, Russ. Math. Surv., 28 (5) (1973), 87-132. | Zbl
, and ,