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Ban, Dubravka.

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p-adic banach space representations = with applications to principal series /

Record Type:	Electronic resources : Monograph/item
Title/Author:	p-adic banach space representations/ by Dubravka Ban.
Reminder of title:	with applications to principal series /
Author:	Ban, Dubravka.
Published:	Cham :Springer Nature Switzerland : : 2022.,
Description:	xii, 214 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Banach spaces. -
Online resource:	https://doi.org/10.1007/978-3-031-22684-7
ISBN:	9783031226847

p-adic banach space representations = with applications to principal series /
Ban, Dubravka.

p-adic banach space representationswith applications to principal series /[electronic resource] :by Dubravka Ban. - Cham :Springer Nature Switzerland :2022. - xii, 214 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23251617-9692 ;. - Lecture notes in mathematics ;v. 2325..

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.

ISBN: 9783031226847

Standard No.: 10.1007/978-3-031-22684-7doiSubjects--Topical Terms:

579190
Banach spaces.

LC Class. No.: QA322.2

Dewey Class. No.: 515.732

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300 $a xii, 214 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2325
520 $a 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.
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