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Ottawa Lectures on Admissible Representations of Reductive $p$-adic Groups

Edited by: Clifton Cunningham University of Calgary, Calgary, AB, Canada
Monica Nevins University of Ottawa, Ottawa, ON, Canada
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4493-9
Product Code: FIM/26
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Electronic ISBN: 978-1-4704-1789-5 Product Code: FIM/26.E List Price:$73.00
MAA Member Price: $65.70 AMS Member Price:$58.40
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List Price: $117.00 MAA Member Price:$105.30
AMS Member Price: $93.60 Click above image for expanded view Ottawa Lectures on Admissible Representations of Reductive$p$-adic Groups Edited by: Clifton Cunningham University of Calgary, Calgary, AB, Canada Monica Nevins University of Ottawa, Ottawa, ON, Canada A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-4493-9 Product Code: FIM/26  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
 Electronic ISBN: 978-1-4704-1789-5 Product Code: FIM/26.E
 List Price: $73.00 MAA Member Price:$65.70 AMS Member Price: $58.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$117.00 MAA Member Price: $105.30 AMS Member Price:$93.60
• Book Details

Fields Institute Monographs
Volume: 262009; 199 pp
MSC: Primary 22; Secondary 14; 11;

Ottawa Lectures offers researchers and graduate students a rare introduction to some of the major modern themes in the representation theory of $p$-adic groups: the classification and construction of their (complex) admissible representations, the calculation of their characters, and the realization of the celebrated local Langlands correspondence. Recent years have seen significant and rapid progress made toward each of these goals; the purpose of this book is to help bridge the gap from the classical literature to the forefront of research.

The first part of this volume is devoted to the tools and techniques used to classify and construct smooth representations of $p$-adic groups: the Bernstein decomposition, Bruhat–Tits theory and filtrations of subgroups, and an overview of J.-K. Yu's construction of supercuspidal representations, together with J.-L. Kim's proof that it is exhaustive. The second part begins with a historical overview of character computations and continues with an introduction to motivic integration. The volume concludes, in the third part, with an introduction to the local Langlands programme and a proof of the local Langlands correspondence for algebraic tori.

The chapters, written by leaders in this field, arose from lecture notes of mini-courses delivered at workshops held at the University of Ottawa in 2004 and 2007.

Graduate students and research mathematicians interested in representation theory of $p$-adic groups.

• Smooth representations
• Chapter 1. The Bernstein decomposition and the Bernstein centre
• Chapter 2. Bruhat–Tits theory and buildings
• Chapter 3. Supercuspidal representations: Construction and exhaustion
• Character theory
• Chapter 4. Character theory of reductive $p$-adic groups
• Chapter 5. An overview of arithmetic motivic integration
• Local Langlands correspondence
• Chapter 6. Notes on the local Langlands program
• Chapter 7. On the local Langlands correspondence for tori

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 262009; 199 pp
MSC: Primary 22; Secondary 14; 11;

Ottawa Lectures offers researchers and graduate students a rare introduction to some of the major modern themes in the representation theory of $p$-adic groups: the classification and construction of their (complex) admissible representations, the calculation of their characters, and the realization of the celebrated local Langlands correspondence. Recent years have seen significant and rapid progress made toward each of these goals; the purpose of this book is to help bridge the gap from the classical literature to the forefront of research.

The first part of this volume is devoted to the tools and techniques used to classify and construct smooth representations of $p$-adic groups: the Bernstein decomposition, Bruhat–Tits theory and filtrations of subgroups, and an overview of J.-K. Yu's construction of supercuspidal representations, together with J.-L. Kim's proof that it is exhaustive. The second part begins with a historical overview of character computations and continues with an introduction to motivic integration. The volume concludes, in the third part, with an introduction to the local Langlands programme and a proof of the local Langlands correspondence for algebraic tori.

The chapters, written by leaders in this field, arose from lecture notes of mini-courses delivered at workshops held at the University of Ottawa in 2004 and 2007.

Graduate students and research mathematicians interested in representation theory of $p$-adic groups.

• Smooth representations
• Chapter 1. The Bernstein decomposition and the Bernstein centre
• Chapter 2. Bruhat–Tits theory and buildings
• Chapter 3. Supercuspidal representations: Construction and exhaustion
• Character theory
• Chapter 4. Character theory of reductive $p$-adic groups
• Chapter 5. An overview of arithmetic motivic integration
• Local Langlands correspondence
• Chapter 6. Notes on the local Langlands program
• Chapter 7. On the local Langlands correspondence for tori
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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