局部群表示论,θ对应和Langlands-Shahidi方法
局部群表示论,θ对应和Langlands-Shahidi方法封面图

局部群表示论,θ对应和Langlands-Shahidi方法

叶扬波, 田野, 编著

出版社:科学出版社

年代:2013

定价:45.0

书籍简介:

本书的5篇文章均由2011年6月在北京晨兴数学中心举办的群表示论研讨会的讲稿补充或重写而成,作者都是国际上数论与群表示论方面的著名专家。CorinneBlondel、ColinJ.Bushnell和VincentSécherre的文章从不同的角度由浅入深地阐述了局部群表示理论的最新发展。DavidManderscheid的文章介绍了局部θ对应理论,而FreydoonShahidi的文章则着重论述了Eisenstein级数理论。这些文章都可以作为Langlands纲领的相关领域的入门与深造的重要必读文献。

书籍目录:

Preface

1 Arithmetic of Cuspidal Representations

1.1 Cuspidal representations by induction

1.1.1 Background and notation

1.1.2 Intertwining and Hecke algebras

1.1.3 Compact induction

1.1.4 An example

1.1.5 A broader context

1.2 Lattices, orders and strata

1.2.1 Lattices and orders

1.2.2 Lattice chains..

1.2.3 Multiplicative structures

1.2.4 Duality

1.2.5 Strata and intertwining

1.2.6 Field extensions

1.2.7 Minimal elements

1.3 Fundamental strata

1.3.1 Fundamental strata

1.3.2 Application to representations

1.3.3 The characteristic polynomial

1.3.4 Nonsplit fundamental strata

1.4 Prime dimension

1.4.1 A trivial case

1.4.2 The general case

1.4.3 The inducing representation

1.4.4 Uniqueness

1.4.5 Summary

1.5 Simple strata and simple characters

1.5.1 Adjoint map

1.5.2 Critical exponent

1.5.3 Construction

1.5.4 Intertwining.

1.5.5 Definitions

1.5.6 Interwining

1.5.7 Motility... ,

1.6 Structure of cuspidal representations

1.6.1 Trivial simple characters

1.6.2 Occurrence of a simple character

1.6.3 Heisenberg representations

1.6.4 A further restriction

1.6.5 End of the road

1.7 Endo-equivalence and lifting

1.7.1 Transfer of simple characters

1.7.2 Endo-equivalence

1.7.3 Invariants

1.7.4 Tame lifting

1.7.5 Tame induction map for endo-classes

1.8 Relation with the Langlands correspondence

1.8.1 The Weil group'

1.8.2 Representations

1.8.3 The Langlands correspondence

1.8.4 Relation with tame lifting

1.8.5 Ramification Theorem

References

2 Basic Representation Theory of Reductive p-adic Groups

2.1 Smooth representations of locally profinite groups

2.1.1 Locally profinite groups

2.1.2 Basic representation theory

2.1.3 Smooth representations

2.1.4 Induced representations

2.2 Admissible representations of locally profinite groups"

2.2.1 Admissible representations

2.2.2 Haar measure

2.2.3 Hecke algebra of a locally profinite group

2.2.4 Coinvariants

2.3 Schur's Lemma and Z-compact representations

2.3.1 Characters

2.3.2 Schur's Lemma and central character

2.3.3 Z-compact representations

2.3.4 An example

……

3 The Bernstein Decomposition for Smooth Complex Representationsof GLn,(F)

4 Lectures on the Local Theta Correspondence

5 An Overview of the Theory of Eisenstein Series

内容摘要:

This book is the first volume of the Lecture Series of Modern, Number Theory, which is devoted to publishing peer-reviewed workshop lecture notes and the proceedings of conferences on all branches of contemporary number theory research. The series intends to target number theory researchers and students, including both experts and non-experts of the covered subjects.

书籍规格:

书籍详细信息
书名局部群表示论,θ对应和Langlands-Shahidi方法站内查询相似图书
9787030380326
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出版地北京出版单位科学出版社
版次1版印次1
定价(元)45.0语种英文
尺寸24 × 17装帧平装
页数 140 印数

书籍信息归属:

局部群表示论,θ对应和Langlands-Shahidi方法是科学出版社于2013.7出版的中图分类号为 O152 的主题关于 群论-研究-英文 的书籍。