On the loop inequality for euclidean buildings

Jacek Świątkowski

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1175-1194
  • ISSN: 0373-0956

Abstract

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We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on A ˜ n groups, as shown in the paper by A. Valette [same issue].

How to cite

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Świątkowski, Jacek. "On the loop inequality for euclidean buildings." Annales de l'institut Fourier 47.4 (1997): 1175-1194. <http://eudml.org/doc/75258>.

@article{Świątkowski1997,
abstract = {We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on $\widetilde\{A\}_n$ groups, as shown in the paper by A. Valette [same issue].},
author = {Świątkowski, Jacek},
journal = {Annales de l'institut Fourier},
keywords = {euclidean building},
language = {eng},
number = {4},
pages = {1175-1194},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the loop inequality for euclidean buildings},
url = {http://eudml.org/doc/75258},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Świątkowski, Jacek
TI - On the loop inequality for euclidean buildings
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1175
EP - 1194
AB - We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on $\widetilde{A}_n$ groups, as shown in the paper by A. Valette [same issue].
LA - eng
KW - euclidean building
UR - http://eudml.org/doc/75258
ER -

References

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  1. [Bo] N. BOURBAKI, Groupes et algèbres de Lie, Chapitres 4-6, Masson, Paris, 1981. Zbl0483.22001
  2. [Br] K. BROWN, Buildings, Springer-Verlag, New York, 1989. Zbl0715.20017MR90e:20001
  3. [CS] D. CARTWRIGHT, T. STEGER, A family of Ãn groups, Preprint. Zbl0923.51010
  4. [T] J. TITS, Buildings of spherical type and finite BN-pairs, Lecture Notes in Math. 386, Springer-Verlag, 1974. Zbl0295.20047MR57 #9866
  5. [V] A. VALETTE, On the Haagerup inequality and groups acting on Ãn-buildings, Ann. Inst. Fourier, Grenoble, 47-4 (1997), 1195-1208. Zbl0886.51003MR99f:43001

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