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A HAAGERUP INEQUALITY, DEFORMATION OF TRIANGLES AND AFFINE BUILDINGS

Published online by Cambridge University Press:  18 January 2006

Malik Talbi
Malik Talbi
Affiliation:
Westfälische Wilhelms-Universität Münster, Mathematisches Institut, Einsteinstraβe 62, 48149 Münster, Germany (talbi@math.uni-muenster.de) Present address: Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France (talbi@math.univ-lyon1.fr)
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Abstract

In this paper we study a Haagerup inequality in the general case of discrete groupoids. We develop two geometrical tools, pinching and tetrahedral change of faces, based on deformation of triangles, to prove it. We show how to use these tools to find all the already known results just by manipulating triangles. We use these tools for groups acting freely and by isometries on the set of vertices of any affine building and give a first reduction of this inequality to its verification on some special triangles and prove the inequality when the building is of type $\tilde{A}_{k_1}\times\cdots\times\tilde{A}_{k_n}$, where $k_i\in\{1,2\}$, $i=1,\dots,n$.

Keywords

property of rapid decay (RD)groups acting on buildingsgroupoidsgeometry of groupsPrimary 20E42Secondary 46L9920F65
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 2 , April 2006 , pp. 187 - 227
Copyright
2006 Cambridge University Press

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