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The chapter develops the theory of K-spherical functions on a group G of p-adic type, with K a compact subgroup of G. It studies the Hecke algebra of compactly supported, K-bi-invariant functions on G, establishes the commutativity of this algebra and constructs the corresponding Satake transform. The additional sections contain several generalizations and applications of these results.

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Spherical functions on a group of p-adic type

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  • 发表日期：

    2026年

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  • Ian G. Macdonald,
  • Anne-Marie Aubert

摘要

The chapter develops the theory of K-spherical functions on a group G of p-adic type, with K a compact subgroup of G. It studies the Hecke algebra of compactly supported, K-bi-invariant functions on G, establishes the commutativity of this algebra and constructs the corresponding Satake transform. The additional sections contain several generalizations and applications of these results.