p-adic Banach Space Representations: With Applications to Principal Series

This book develops the theory of continuous representations on p-adic Banach spaces, laying the foundations for representation theory of reductive p-adic groups and applications to continuous principal series. It is accessible to graduate students and provides a comprehensive introduction to the necessary tools.

Format: Paperback / softback
Length: 214 pages
Publication date: 01 February 2023
Publisher: Springer International Publishing AG

This book is a comprehensive exploration of the theory of continuous representations on p-adic Banach spaces, with the primary objective of establishing the foundations for the representation theory of reductive p-adic groups on these spaces. It also aims to elucidate the duality theory of Schneider and Teitelbaum and demonstrate its practical applications to continuous principal series. Written with graduate students in mind, the book provides a thorough introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 concludes with a profound duality between Banach space representations and Iwasawa modules, which is then applied in Part 2 to study the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph serves as both a valuable reference for experts in the field and an essential introductory text for graduate students and researchers seeking to delve into this captivating area of mathematics.

Weight: 355g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031226830
Edition number: 1st ed. 2022