Group-theoretic compactification of Bruhat–Tits buildings
Annales scientifiques de l'École Normale Supérieure (2006)
- Volume: 39, Issue: 6, page 871-920
- ISSN: 0012-9593
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topGuivarc'h, Yves, and Rémy, Bertrand. "Group-theoretic compactification of Bruhat–Tits buildings." Annales scientifiques de l'École Normale Supérieure 39.6 (2006): 871-920. <http://eudml.org/doc/82703>.
@article{Guivarch2006,
author = {Guivarc'h, Yves, Rémy, Bertrand},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {semisimple groups; non-Archimedean local fields; Bruhat-Tits buildings; Chabauty topology; polyhedral compactifications; amenable subgroups; distal subgroups; geometric parametrizations of subgroups; convergence theorems; parabolic subgroups; maximal compact subgroups; Euclidean buildings; semi-homogeneous trees},
language = {eng},
number = {6},
pages = {871-920},
publisher = {Elsevier},
title = {Group-theoretic compactification of Bruhat–Tits buildings},
url = {http://eudml.org/doc/82703},
volume = {39},
year = {2006},
}
TY - JOUR
AU - Guivarc'h, Yves
AU - Rémy, Bertrand
TI - Group-theoretic compactification of Bruhat–Tits buildings
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2006
PB - Elsevier
VL - 39
IS - 6
SP - 871
EP - 920
LA - eng
KW - semisimple groups; non-Archimedean local fields; Bruhat-Tits buildings; Chabauty topology; polyhedral compactifications; amenable subgroups; distal subgroups; geometric parametrizations of subgroups; convergence theorems; parabolic subgroups; maximal compact subgroups; Euclidean buildings; semi-homogeneous trees
UR - http://eudml.org/doc/82703
ER -
References
top- [1] Adams S., Ballmann W., Amenable isometry groups of Hadamard spaces, Math. Ann.312 (1998) 183-195. Zbl0913.53012MR1645958
- [2] Abels H., Distal affine transformation groups, J. reine angew. Math.299 (1978) 294-300. Zbl0367.20047MR470944
- [3] Abels H., Distal automorphism groups of Lie groups, J. reine angew. Math.329 (1981) 82-87. Zbl0463.22006MR636446
- [4] Allcock D., Carlson J.A., Toledo D., The complex hyperbolic geometry of the moduli space of cubic surfaces, J. Algebraic Geometry11 (2002) 659-724. Zbl1080.14532MR1910264
- [5] Ash A., Mumford D., Rapoport M., Tai Y.S., Smooth Compactification of Locally Symmetric Spaces, Lie Groups: History, Frontiers and Applications, vol. IV, Math. Sci. Press, Brookline, MA, 1975. Zbl0334.14007MR457437
- [6] Baily W.L., Borel A., Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math.84 (1966) 442-528. Zbl0154.08602MR216035
- [7] Behr H., Higher finiteness properties of S-arithmetic groups in the function field case I, in: Müller T.W. (Ed.), Groups: Topological, Combinatorial and Arithmetic Aspects, London Math. Soc. Lecture Notes Series, vol. 311, Cambridge University Press, 2004, pp. 27-42. Zbl1099.20022MR2073345
- [8] Bridson M., Haefliger A., Metric Spaces of Non-Positive Curvature, Grund. Math. Wiss., vol. 319, Springer, 1999. Zbl0988.53001MR1744486
- [9] Borel A., Ji L., Compactifications of Symmetric and Locally Symmetric Spaces, Mathematics: Theory & Applications, Birkhäuser, 2006. Zbl1100.22001MR2189882
- [10] Burger M., Mozes S., -spaces, divergence groups and their commensurators, J. Amer. Math. Soc.9 (1996) 57-93. Zbl0847.22004MR1325797
- [11] Burger M., Mozes S., Groups acting on trees: from local to global structure, Publ. Math. IHÉS92 (2000) 113-150. Zbl1007.22012MR1839488
- [12] Borel A., Linear Algebraic Groups, Graduate Texts in Math., vol. 126, Springer, 1991. Zbl0726.20030MR1102012
- [13] Bourbaki N., Intégration VII–VIII, Éléments de Mathématique, Hermann, 1963. MR453824
- [14] Bourbaki N., Topologie générale I–IV, Éléments de Mathématique, Hermann, 1971. Zbl0249.54001MR358652
- [15] Bourbaki N., Algèbre VIII, Éléments de Mathématique, Hermann, 1973. MR417224
- [16] Bourbaki N., Groupes et algèbres de Lie IV–VI, Éléments de Mathématique, Masson, 1981. Zbl0483.22001MR647314
- [17] Brown K.S., Buildings, Springer, 1989. Zbl0715.20017MR969123
- [18] Borel A., Serre J.-P., Corners and arithmetic groups, Comm. Math. Helv.48 (1973) 463-491. Zbl0274.22011MR387495
- [19] Borel A., Serre J.-P., Cohomologie d'immeubles et de groupes S-arithmétiques, Topology15 (1976) 211-232. Zbl0338.20055MR447474
- [20] Borel A., Tits J., Groupes réductifs, Publ. Math. IHÉS27 (1965) 55-150. Zbl0145.17402MR207712
- [21] Borel A., Tits J., Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I, Invent. Math.12 (1971) 95-104. Zbl0238.20055MR294349
- [22] Bruhat F., Tits J., Groupes réductifs sur un corps local, I. Données radicielles valuées, Publ. Math. IHÉS41 (1972) 5-251. Zbl0254.14017MR327923
- [23] Borel A., Tits J., Homomorphismes « abstraits » de groupes algébriques simples, Ann. of Math.97 (1973) 499-571. Zbl0272.14013MR316587
- [24] Bruhat F., Tits J., Groupes réductifs sur un corps local, II. Schémas en groupes. Existence d'une donnée radicielle valuée, Publ. Math. IHÉS60 (1984) 197-376. Zbl0597.14041MR756316
- [25] Bruhat F., Tits J., Schémas en groupes et immeubles des groupes classiques sur un corps local, Bull. Soc. Math. France112 (1984) 259-301. Zbl0565.14028MR788969
- [26] Canary R.D., Epstein D.B.A., Green P., Notes on notes of Thurston, in: Epstein D.B.A. (Ed.), Analytical and Geometrical Aspects of Hyperbolic Spaces, London Math. Soc. Lecture Notes Series, vol. 111, Cambridge University Press, 1987. Zbl0612.57009MR903850
- [27] Conze J.-P., Guivarc'h Y., Remarques sur la distalité dans les espaces vectoriels, C. R. Acad. Sci. Paris278 (1974) 1083-1086. Zbl0275.54028MR339108
- [28] de Cornulier Y., Invariant means on projective spaces, Preprint, 2004.
- [29] Figá-Talamanca A., Nebbia C., Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, London Math. Soc. Lecture Notes Series, vol. 162, Cambridge University Press, 1991. Zbl1154.22301MR1152801
- [30] Furstenberg H., The structure of distal flows, Amer. J. Math.85 (1963) 477-515. Zbl0199.27202MR157368
- [31] Furstenberg H., Boundary theory and stochastic processes on homogeneous spaces, in: Moore C.C. (Ed.), Harmonic Analysis on Homogeneous Spaces, Proc. Symp. Pure Math., vol. XXVI, AMS, Providence, RI, 1972, pp. 193-229. Zbl0289.22011MR352328
- [32] Ghys É., de la Harpe P., Sur les groupes hyperboliques d'après Mikhael Gromov, Progr. Math., vol. 83, Birkhäuser, 1990. Zbl0731.20025MR1086648
- [33] Goldman O., Iwahori N., The space of p-adic norms, Acta Math.109 (1963) 137-177. Zbl0133.29402MR144889
- [34] Gille P., Unipotent subgroups of reductive groups in characteristic , Duke Math. J.114 (2002) 307-328. Zbl1013.20040MR1920191
- [35] Guivarc'h Y., Compactifications of symmetric spaces and positive eigenfunctions of the Laplacian, in: Taylor J.Ch. (Ed.), Topics in Probability and Lie Groups; Boundary Theory, CRM Proc. Lect. Notes, vol. 28, AMS, 2001, pp. 69-116. Zbl1160.58306MR1832435
- [36] Guivarc'h Y., Ji L., Taylor J.Ch., Compactifications of Symmetric Spaces, Progr. Math., vol. 156, Birkhäuser, 1998. Zbl1053.31006MR1633171
- [37] Landvogt E., A Compactification of the Bruhat–Tits Building, Lecture Notes in Math., vol. 1619, Springer, 1996. Zbl0935.20034MR1441308
- [38] Lubotzky A., Mozes S., Asymptotic properties of unitary representations of tree automorphisms, in: Piccardello M. (Ed.), Harmonic Analysis and Discrete Potential Theory (Frascati, 1991), Plenum Press, New York, 1992, pp. 289-298. MR1222467
- [39] Lubotzky A., Mozes S., Zimmer R.J., Superrigidity for the commensurability group of tree lattices, Comm. Math. Helv.69 (1994) 523-548. Zbl0839.22011MR1303226
- [40] Mackey G.W., Induced representations of locally compact groups I, Ann. of Math.55 (1952) 101-139. Zbl0046.11601MR44536
- [41] Margulis G.A., Discrete Subgroups of Semisimple Lie Groups, Ergeb. Math. Grenzgeb. (3), vol. 17, Springer, 1991. Zbl0732.22008MR1090825
- [42] Moore C.C., Compactifications of symmetric spaces, Amer. J. Math.86 (1964) 201-218. Zbl0156.03202MR161942
- [43] Moore C.C., Amenable subgroups of semisimple groups and proximal flows, Israel J. Math.34 (1979) 121-138. Zbl0431.22014MR571400
- [44] Platonov V., Rapinchuk A., Algebraic Groups and Number Theory, Pure Appl. Math., vol. 139, Academic Press, 1994. Zbl0841.20046MR1278263
- [45] Prasad G., Elementary proof of a theorem of Bruhat–Tits–Rousseau and of a theorem of Tits, Bull. Soc. Math. France110 (1982) 197-202. Zbl0492.20029MR667750
- [46] Raghunathan M.S., Discrete Subgroups of Lie Groups, Ergeb. Math. Grenzgeb., vol. 68, Springer, 1972. Zbl0254.22005MR507234
- [47] Ronan M.A., Lectures on Buildings, Perspectives in Mathematics, vol. 7, Academic Press, 1989. Zbl0694.51001MR1005533
- [48] Rousseau G., Immeubles des groupes réductifs sur les corps locaux, thèse d'État, Université de Paris-Sud (Orsay), 1977. Zbl0412.22006MR491992
- [49] Satake I., On compactifications of the quotient spaces for arithmetically defined discontinuous groups, Ann. of Math.72 (1960) 555-580. Zbl0146.04701MR170356
- [50] Satake I., On representations and compactifications of symmetric Riemannian spaces, Ann. of Math.71 (1960) 77-110. Zbl0094.34603MR118775
- [51] Springer T.A., Linear Algebraic Groups, Progr. Math., vol. 9, Birkhäuser, 1998. Zbl0453.14022MR1642713
- [52] Tits J., Free subgroups in linear groups, J. Algebra20 (1972) 250-270. Zbl0236.20032MR286898
- [53] Tits J., Reductive groups over local fields, in: Borel A., Casselman W.A. (Eds.), Automorphic Forms, Representations and L-Functions, Proc. Symp. Pure Math. (Oregon State Univ., Corvallis, 1977), part 1, vol. XXXIII, AMS, Providence, RI, 1979, pp. 29-69. Zbl0415.20035MR546588
- [54] Werner A., Compactification of the Bruhat–Tits building of PGL by lattices of smaller rank, Doc. Math.6 (2001) 315-341. Zbl1048.20014MR1871666
- [55] Werner A., Compactification of the Bruhat–Tits building of PGL by seminorms, Math. Z.248 (2004) 511-526. Zbl1121.20024MR2097372
- [56] Zimmer R.J., Ergodic Theory and Semisimple Groups, Monographs Math., vol. 81, Birkhäuser, 1984. Zbl0571.58015MR776417
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