叶扬波、田野编著的《局部群表示论(θ-对应和Langlands-Shahidi方法》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。

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 Indamental 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

 2.4 Cuspidal representations of reductive p-adic groups

2.4.1 Parabolic induction and restriction

2.4.2 Parabolic pairs

2.4.3 Cuspidal representations

2.4.4 Iwahori decomposition

2.4.5 Smooth irreducible representations are admissible

 References

3 The Bernstein Decomposition for Smooth Complex Representationsof GL(F)

 3.1 Compact representations

3.1.1 The decomposition theorem

3.1.2 Formal degree of an irreducible compact representation

3.1.3 Proof of Theorem 1.3

3.1.4 The compact part of a smooth representation of H

 3.2 The cuspidal part of a smooth representation

3.2.1 From compact to cuspidal representations

3.2.2 The group H satisfies the finiteness condition

3.2.3 The cuspidal part of a smooth representation

 3.3 The noncuspidal part of a smooth representation

3.3.1 The cuspidal support of an irreducible representation

3.3.2 The decomposition theorem

3.3.3 Further questions

 3.4 Modular smooth representations of GLn(F)

3.4.1 Thelpcase

3.4.2 The 1 --- p case

 References

4 Lectures on the Local Theta Correspondence

 4.1 Lecture 1

4.1.1 The Heisenberg group

4.1.2 The Weil representation

4.1.3 Dependence on

4.1.4 Now suppose that W1 and W2 are symplectic spaces over

4.1.5 Models of Pe and

 4.2 Lecture 2

4.2.1 (Reductive) dual pairs

4.2.2 Theta correspondence

4.2.3 An explicit model

 4.3 Lecture 3

4.3.1 Explicit models of the Weil representation

4.3.2 Low dimensional examples

4.3.3 General (conjectural) framework

 References

5 An Overview of the Theory of Eisenstein Series

 5.1 Intertwining operators

 5.2 Definitions and the statement of the main theorem

 5.3 Constant term

 5.4 Proof of meromorphic continuation for the rank one case

5.4.1 Preliminaries

5.4.2 Truncation

5.4.3 Truncation of ET

5.4.4 The functionM equation for AT o E

5.4.5 Proof of meromorphic continutation

 5.5 Proof of the functional equation

 5.6 Convergence of Eisenstein series

 5.7 Proof of holomorphy for p Cia

 References

Index