264 research outputs found
Buildings and Hecke algebras
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
Shadows in Coxeter groups
For a given in a Coxeter group the elements smaller than in
Bruhat order can be seen as the end-alcoves of stammering galleries of type
in the Coxeter complex . We generalize this notion and consider sets of
end-alcoves of galleries that are positively folded with respect to certain
orientation of . We call these sets shadows. Positively folded
galleries are closely related to the geometric study of affine Deligne-Lusztig
varieties, MV polytopes, Hall-Littlewood polynomials and many more agebraic
structures. In this paper we will introduce various notions of orientations and
hence shadows and study some of their algorithmic properties.Comment: 30 pages, 8 figures, revised and final versio
- …