Ottawa Lectures on Admissible Representations of Reductive $p$-adic Groups (Fields Institute Monographs, 26)

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.