Buildings and Hecke algebras
By James Parkinson. 2006
74 citations recorded by the source corpus.
Abstract In this paper we establish a strong connection between buildings and Hecke algebras by studying two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. We show that for appropriately parametrised Hecke algebras H and H ˜ , the algebra B is isomorphic to H and the algebra A is isomorphic to the centre of H ˜ . On the one hand these results give a thorough understanding of the algebras A and B . On the other hand they give a nice geometric and combinatorial understanding of Hecke algebras, and in particular of the Macdonald spherical functions and the centre of affine Hecke algebras. Our results also produce interesting examples of association schemes and polynomial hypergroups. In later work we use the results here to study random walks on affine buildings.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/166aa8e3ab68ceab8327a3772566a4126d51fbeb
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra (2005, methodology): “rguments using the affine Grassmanian of the Langlands dual G of G∨ to calculate the degree and the leading coefficients of Cν λµ. Another interpretation of the structure constants was given by Parkinson [Par06] using regular affine buildings. 5 Satake coefficients In this section we introduce the alcove ba”