Property (T) and A ¯ 2 groups

Donald I. Cartwright; Wojciech Młotkowski; Tim Steger

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 1, page 213-248
  • ISSN: 0373-0956

Abstract

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We show that each group Γ in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of Γ with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers to (in [9]), p. 133, Questions 1 and 2.

How to cite

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Cartwright, Donald I., Młotkowski, Wojciech, and Steger, Tim. "Property (T) and $\overline{A}_2$ groups." Annales de l'institut Fourier 44.1 (1994): 213-248. <http://eudml.org/doc/75056>.

@article{Cartwright1994,
abstract = {We show that each group $\Gamma $ in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of $\Gamma $ with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers to (in [9]), p. 133, Questions 1 and 2.},
author = {Cartwright, Donald I., Młotkowski, Wojciech, Steger, Tim},
journal = {Annales de l'institut Fourier},
keywords = {finitely generated groups; Kazhdan’s property (); Kazhdan constant},
language = {eng},
number = {1},
pages = {213-248},
publisher = {Association des Annales de l'Institut Fourier},
title = {Property (T) and $\overline\{A\}_2$ groups},
url = {http://eudml.org/doc/75056},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Cartwright, Donald I.
AU - Młotkowski, Wojciech
AU - Steger, Tim
TI - Property (T) and $\overline{A}_2$ groups
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 1
SP - 213
EP - 248
AB - We show that each group $\Gamma $ in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of $\Gamma $ with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers to (in [9]), p. 133, Questions 1 and 2.
LA - eng
KW - finitely generated groups; Kazhdan’s property (); Kazhdan constant
UR - http://eudml.org/doc/75056
ER -

References

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Citations in EuDML Documents

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  1. Sylvain Barré, Immeubles de Tits triangulaires exotiques
  2. Sylvain Barré, Sur les polyèdres de rang 2
  3. Alain Valette, On the Haagerup inequality and groups acting on A ˜ n -buildings
  4. Alain Valette, Graphes de Ramanujan et applications
  5. Pierre Pansu, Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles
  6. Yehuda Shalom, Explicit Kazhdan constants for representations of semisimple and arithmetic groups
  7. Alain Valette, Nouvelles approches de la propriété (T) de Kazhdan

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