Lecture Notes in Mathematics: With Applications to Principal Series

Ban, Dubravka

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.

Details

Published by: Springer

Publication Date: 2023-02-12

Format: Paperback

ISBN-13: 9783031226830

DOI: 10.1007/978-3-031-22684-7

Dimensions: 235cm x155cm

Pages: 214