Softcover ISBN:  9780821807095 
Product Code:  CBMS/59 
76 pp 
List Price:  $27.00 
Individual Price:  $21.60 
Electronic ISBN:  9781470424206 
Product Code:  CBMS/59.E 
76 pp 
List Price:  $25.00 
Individual Price:  $20.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 59; 1985MSC: Primary 22; Secondary 20;
This book introduces a systematic new approach to the construction and analysis of semisimple \(p\)adic groups. The basic construction presented here provides an analogue in certain cases of the HarishChandra homomorphism, which has played an essential role in the theory of semisimple Lie groups. The book begins with an overview of the representation theory of GL\(_n\) over finite groups. The author then explicitly establishes isomorphisms between certain convolution algebras of functions on two different groups. Because of the form of the isomorphisms, basic properties of representations are preserved, thus giving a concrete example to the correspondences predicted by the general philosphy of Langlands.
The first chapter, suitable as an introduction for graduate students, requires only a basic knowledge of representation theory of finite groups and some familiarity with the general linear group and the symmetric group. The later chapters introduce researchers in the field to a new method for the explicit construction and analysis of representations of \(p\)adic groups, a powerful method clearly capable of extensive further development.Readership 
Table of Contents

Chapters

Chapter 1. A Hecke Algebra Approach to the Representations of GL$_n(\mathbb {F}_q)$

Chapter 2. Hecke Algebras for GL$_n$ over Local Fields: Introduction

Chapter 3. The HarishChandra Homomorphism in the Unramified Anisotropic Case

Appendix 1. Plancherel Measure and Hecke Algebras

Appendix 2. The Representation Ind$_B^G$1

Appendix 3. Cuspidal Representations of GL$_n(\mathbb {F}_q)$


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 Table of Contents

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This book introduces a systematic new approach to the construction and analysis of semisimple \(p\)adic groups. The basic construction presented here provides an analogue in certain cases of the HarishChandra homomorphism, which has played an essential role in the theory of semisimple Lie groups. The book begins with an overview of the representation theory of GL\(_n\) over finite groups. The author then explicitly establishes isomorphisms between certain convolution algebras of functions on two different groups. Because of the form of the isomorphisms, basic properties of representations are preserved, thus giving a concrete example to the correspondences predicted by the general philosphy of Langlands.
The first chapter, suitable as an introduction for graduate students, requires only a basic knowledge of representation theory of finite groups and some familiarity with the general linear group and the symmetric group. The later chapters introduce researchers in the field to a new method for the explicit construction and analysis of representations of \(p\)adic groups, a powerful method clearly capable of extensive further development.

Chapters

Chapter 1. A Hecke Algebra Approach to the Representations of GL$_n(\mathbb {F}_q)$

Chapter 2. Hecke Algebras for GL$_n$ over Local Fields: Introduction

Chapter 3. The HarishChandra Homomorphism in the Unramified Anisotropic Case

Appendix 1. Plancherel Measure and Hecke Algebras

Appendix 2. The Representation Ind$_B^G$1

Appendix 3. Cuspidal Representations of GL$_n(\mathbb {F}_q)$