局部群表示论，θ对应和Langlands-Shahidi方法

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

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.