Aubert A.-M., Mishra M., Roche A., Spallone S. (Eds.) Representations of Reductive p-adic Groups: International Conference, IISER, Pune, India, 2017

Springer, 2019. — 297 p. — (Progress in Mathematics 328). — ISBN: 978-981-13-6627-7.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.Local Langlands and Springer Correspondences
Arithmetic of Cuspidal Representations
Root Data with Group Actions
The Character of a Simple Supercuspidal Representation of SL(2, F)
Classification of Strongly Positive Representations of Even General Unitary Groups
On the Unicity of Types for Toral Supercuspidal Representations
Local Gamma Factors, Converse Theorems and Related Problems
On Completions of Hecke Algebras
On Relatively Tempered Representations for p-adic Symmetric Spaces