局部群表示论,θ对应和Langlands-Shahidi方法

书籍目录

Preface

1Arithmetic of Cuspidal Representations

1.1Cuspidal representations by induction

1.1.1Background and notation

1.1.2Intertwining and Hecke algebras

1.1.3Compact induction

1.1.4An example

1.1.5A broader context

1.2Lattices,orders and strata

1.2.1Lattices and orders

1.2.2Lattice chains

1.2.3Multiplicatives tructures

1.2.4Duality

1.2.5Strata and intertwining

1.2.6Field extensions

1.2.7Minimal elements

1.3Fundamental strata

1.3.1Indamental strata

1.3.2Application to representations

1.3.3The characteristic polynomial

1.3.4Nonsplit fundamental strata

1.4Prime dimension

1.4.1A trivial case

1.4.2The general case

1.4.3The inducing representation

1.4.4Uniqueness

1.4.5Summary

1.5Simple strata and simple characters

1.5.1Adjoint map

1.5.2Critical exponent

1.5.3Construction

1.5.4Intertwining

1.5.5Definitions

1.5.6Interwining

1.5.7Motility

1.6Structure of cuspidal representations

1.6.1Trivial simple characters

1.6.2Occurrence of a simple character

1.6.3Heisenberg representations

1.6.4A further restriction

1.6.5End of the road

1.7Endo-equivalence and lifting

1.7.1Transfer of simple characters

1.7.2Endo-equivalence

1.7.3Invariants

1.7.4Tame lifting

1.7.5Tame induction map for endo-classes

1.8Relation with the Langlands correspondence

1.8.1The Weil group

1.8.2Representations

1.8.3The Langlands correspondence

1.8.4Relation with tame lifting

1.8.5Ramification Theorem

References

……

2Basic Representation Theory of Reductive p-adic Groups

3The Bernstein Decomposition for Smooth Complex Representations of GLn(F)

4Lectures on the Local Theta Correspondence

5An Overview of the Theory of Eisenstein Series

Index

作者简介

《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。Corinne Blondel、Colin J.Bushnell和Vincent Secherre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。

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