Representations of Reductive p-adic Groups : International Conference, IISER, Pune, India, 2017 / edited by Anne-Marie Aubert, Manish Mishra, Alan Roche, Steven Spallone.

1st ed. 2019.
Singapore : Springer Singapore : Imprint: Birkhäuser, 2019.
Mathematics and Statistics (Springer-11649)
Progress in Mathematics, 0743-1643 ; 328
Progress in Mathematics, 0743-1643 ; 328
1 online resource (XIII, 289 pages) : 4 illustrations, 3 illustrations in color.
Topological groups.
Lie groups.
Group theory.
Harmonic analysis.
Local subjects:
Topological Groups, Lie Groups. (search)
Group Theory and Generalizations. (search)
Abstract Harmonic Analysis. (search)
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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.
Chapter 1: Introduction to the local Langlands correspondence
Chapter 2. Arithmetic of cuspidal representations
Chapter 3. Harmonic analysis and affine Hecke algebras
Chapter 4. Types and Hecke algebras. .
Aubert, Anne-Marie, editor., Editor,
Mishra, Manish, editor., Editor,
Roche, Alan, editor., Editor,
Spallone, Steven, editor., Editor,
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10.1007/978-981-13-6628-4 doi
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