P-Adic Banach Space Representations: With Applications to Principal Series

By Dubravka Ban

This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive 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 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces.
This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.

• Format: Paperback
• Language: English
• ISBN: 3031226836
• ISBN13: 9783031226830
• Release Date: February 2023
• Publisher: Springer
• Length: 214 Pages
• Weight: 0.72 lbs.
• Dimensions: 0.5" x 6.1" x 9.2"