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A HAAGERUP INEQUALITY, DEFORMATION OF TRIANGLES AND AFFINE BUILDINGS
Published online by Cambridge University Press: 18 January 2006
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
- 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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