Buildings and Hecke algebras

Details Buildings and Hecke algebras Buildings and Hecke algebras

2006-04-04

arxiv.org/abs/math/0604056v1

Journal of Algebra 297 (2006) 1-49

Mathematics

Representation Theory

Scientific paper

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.

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