Padic Banach Space Representations With Applications To Principal Series 1st Edition Dubravka Ban by Dubravka Ban 9783031226830, 9783031226847, 3031226836, 3031226844 instant download after payment.

Mathematics Subject Classification: • 22E50 Representations of Lie and linear algebraic groups over local fields • 20G25 Linear algebraic groups over local fields and their integers • 11F70 Representation-theoretic methods; automorphic representations over local and global fields • 11F85 p-adic theory, local fields • 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis

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.