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<div>This is a new, updated edition of a foundational text on the representation theory of <em>p</em>-adic groups.</div><div>&#xa0;</div><div>The book develops the theory of spherical functions for reductive groups defined over nonarchimedean local fields. It provides explicit formulas, studies their properties (positivity, normalization, etc.), and describes a pioneering construction of the spherical transform and the Plancherel formula. This theory underlies the modern theory of affine Hecke algebras, unramified representations of <em>p</em>-adic groups, and the local Langlands program.</div><div>&#xa0;</div><div>This augmented and annotated edition makes a standard reference widely available to contemporary researchers in the representation theory of <em>p</em>-adic groups, automorphic forms, and harmonic analysis on locally compact groups.</div>

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Spherical Functions on a Group of p-adic Type

  • 书籍

  • 发表日期：

    2026年

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  • Ian G. Macdonald,
  • Anne-Marie Aubert

摘要

This is a new, updated edition of a foundational text on the representation theory of p-adic groups.
 
The book develops the theory of spherical functions for reductive groups defined over nonarchimedean local fields. It provides explicit formulas, studies their properties (positivity, normalization, etc.), and describes a pioneering construction of the spherical transform and the Plancherel formula. This theory underlies the modern theory of affine Hecke algebras, unramified representations of p-adic groups, and the local Langlands program.
 
This augmented and annotated edition makes a standard reference widely available to contemporary researchers in the representation theory of p-adic groups, automorphic forms, and harmonic analysis on locally compact groups.