Volume: 26; 2009; 199 pp; Hardcover
MSC: Primary 22; Secondary 14; 11
Print ISBN: 978-0-8218-4493-9
Product Code: FIM/26
List Price: $78.00
AMS Member Price: $62.40
MAA Member Price: $70.20
Electronic ISBN: 978-1-4704-1789-5
Product Code: FIM/26.E
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Ottawa Lectures on Admissible Representations of Reductive \(p\)-adic Groups
Share this pageEdited by Clifton Cunningham; Monica Nevins
A co-publication of the AMS and Fields Institute
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.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Readership
Graduate students and research mathematicians interested in representation theory of \(p\)-adic groups.
Table of Contents
Table of Contents
Ottawa Lectures on Admissible Representations of Reductive $p$-adic Groups
- Cover Cover11
- Title page i3
- Contents iii5
- Preface vii9
- Some background ix11
- Part I. Smooth representations 115
- The Bernstein decomposition and the Bernstein centre 317
- Bruhat–Tits theory and buildings 5367
- Supercuspidal representations: Construction and exhaustion 7993
- Part II. Character theory 101115
- Character theory of reductive 𝑝-adic groups 103117
- An overview of arithmetic motivic integration 113127
- Part III. Local Langlands correspondence 151165
- Notes on the local Langlands program 153167
- On the local Langlands correspondence for tori 177191
- Bibliography 185199
- Index 195209
- Back Cover Back Cover1217