P-Adic Banach Space Representations

P-Adic Banach Space Representations With Applications to Principal Series - Lecture Notes in Mathematics

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Publisher's Synopsis

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.

Book information

ISBN: 9783031226830
Publisher: Springer Nature Switzerland
Imprint: Springer
Pub date:
DEWEY: 515.732
DEWEY edition: 23
Language: English
Number of pages: 214
Weight: 358g
Height: 163mm
Width: 302mm
Spine width: 20mm