数学物理学报(英文版) ›› 2001, Vol. 21 ›› Issue (1): 21-28.

• 论文 • 上一篇    下一篇

HARMONIC ANALYSIS ON THE QUOTIENT k×|×|k\A1 ×|A 1

 Anton Deitmar   

  1. School of Mathematical Sciences University of Exeter
    Laver Building, North Park Road Exeter, EX4 4QE Devon, UK
  • 出版日期:2001-01-06 发布日期:2001-01-06

HARMONIC ANALYSIS ON THE QUOTIENT k×|×|k\A1 ×|A 1

 Anton Deitmar   

  1. School of Mathematical Sciences University of Exeter
    Laver Building, North Park Road Exeter, EX4 4QE Devon, UK
  • Online:2001-01-06 Published:2001-01-06

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摘要：

Let G be the semidirect product A1×A of the adeles and the norm 1 ideles of a global field k. Let ?? be the discrete subgroup k××k. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L2(?? \G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.

关键词: Ideles, adeles, Selberg trace formula, Hecke algebra

Abstract:

Let G be the semidirect product A1×A of the adeles and the norm 1 ideles of a global field k. Let ?? be the discrete subgroup k××k. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L2(?? \G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.

Key words: Ideles, adeles, Selberg trace formula, Hecke algebra

中图分类号: 

  • 11E72
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