2006/04/04 by James Parkinson · 1 citation
Mathematics · #math.RT #msc:20C08 #msc:20E42 #msc:33D52
published as Journal of Algebra 297 (2006) 1-49
arxiv created 2006/04/04 · arxiv updated 2009/12/01
This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description of certain Hecke algebras, and in particular of the Macdonald spherical functions and the center of affine Hecke algebras. The results of this paper are used in later work to study spherical harmonic analysis on affine buildings, and to study isotropic random walks on affine buildings.