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Birkhäuser

Representations of Reductive p-adic Groups

International Conference, IISER, Pune, India, 2017

  • Book
  • © 2019

Overview

Editors:
  1. Anne-Marie Aubert

    1. Institut de Mathématiques de Jussieu, Paris, France

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  2. Manish Mishra

    1. Department of Mathematics, Indian Institute of Science Education and Research Pune, Pune, India

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  3. Alan Roche

    1. Department of Mathematics, University of Oklahoma, Norman, USA

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  4. Steven Spallone

    1. Department of Mathematics, Indian Institute of Science Education and Research Pune, Pune, India

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  • Highlights the latest research on representations of p-adic groups
  • Features survey articles and original research articles by respected experts
  • Presents a survey by Anne-Marie Aubert on the hugely influential local Langlands program
  • Includes a survey by Colin Bushnell on the fine structure of the local Langlands correspondence for general linear groups

Part of the book series: Progress in Mathematics (PM, volume 328)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Local Langlands and Springer Correspondences

    • Anne-Marie Aubert
    Pages 1-37

  3. Arithmetic of Cuspidal Representations

    • Colin J. Bushnell
    Pages 39-126

  4. Root Data with Group Actions

    • Jeffrey D. Adler, Joshua M. Lansky
    Pages 127-143

  5. The Character of a Simple Supercuspidal Representation of SL(2, F)

    • Moshe Adrian
    Pages 145-159

  6. Classification of Strongly Positive Representations of Even General Unitary Groups

    • Yeansu Kim, Ivan Matić
    Pages 161-174

  7. On the Unicity of Types for Toral Supercuspidal Representations

    • Peter Latham, Monica Nevins
    Pages 175-190

  8. Local Gamma Factors, Converse Theorems and Related Problems

    • Chufeng Nien
    Pages 191-205

  9. On Completions of Hecke Algebras

    • Maarten Solleveld
    Pages 207-262

  10. On Relatively Tempered Representations for p-adic Symmetric Spaces

    • Shuichiro Takeda
    Pages 263-289
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Keywords

About this book

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.

Editors and Affiliations

  • Institut de Mathématiques de Jussieu, Paris, France

    Anne-Marie Aubert

  • Department of Mathematics, Indian Institute of Science Education and Research Pune, Pune, India

    Manish Mishra, Steven Spallone

  • Department of Mathematics, University of Oklahoma, Norman, USA

    Alan Roche

About the editors

ANNE-MARIE AUBERT is Research Director in Mathematics at the Centre National de la Recherche Scientifique (CNRS) at the Institut Mathématiques de Jussieu Paris Rive-Gauche, Paris, France. She is a member of the Comité National de la Recherche Scientifique, and has served on the editorial board of the Bulletin and the Memoirs of the French Mathematical Society. 

MANISH MISHRA is Assistant Professor of Mathematics at the Indian Institute of Science Education and Research (IISER), Pune, India. He previously held postdoctoral positions at the Heidelberg University and the Hebrew University of Jerusalem. He completed his BTech at the Indian Institute of Technology Kanpur and his PhD at Purdue University, USA. 

ALAN ROCHE is Associate Professor of Mathematics at the University of Oklahoma, USA. He previously held visiting positions at Purdue University and Oklahoma State University, USA. 

STEVEN SPALLONE is Associate Professor of Mathematics at the IndianInstitute of Science Education and Research (IISER), Pune, India. He graduated from the University of Pennsylvania and completed his PhD at the University of Chicago, USA, in 1998 and 2004, respectively. His research interests include number theory and representation theory.

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