仿射建筑物的球面调和分析
Spherical harmonic analysis on affine buildings
摘要：
每一个正则仿射建筑物都自然地与一个由顶点集平均算子张成的交换代数A相关联。本文研究了从A到复数的代数同态。特别是，我们提供了两个明确的公式，这些同态，一个在麦克唐纳球面函数，另一个作为一个整体的边界上的建设。我们还确定了相应的Plancherel测度，并计算了A的每个基元的l^2-算子范数。
英文摘要：
To each regular affine building there is naturally associated a commutative algebra A spanned by vertex set averaging operators. In this paper we study the algebra homomorphisms from A into the complex numbers. In particular, we provide two explicit formulae for these homomorphisms; one in terms of the Macdonald spherical functions, and another as an integral over the boundary of the building. We also determine the associated Plancherel measure, and we compute the l^2-operator norms of each basis element of A.
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