Product details:
| ISBN13: | 9783031226830 |
| ISBN10: | 3031226836 |
| Binding: | Paperback |
| No. of pages: | 214 pages |
| Size: | 235x155 mm |
| Weight: | 355 g |
| Language: | English |
| Illustrations: | 1 Illustrations, black & white |
| 528 |
Category:
p-adic Banach Space Representations
With Applications to Principal Series
Series:
Lecture Notes in Mathematics;
2325;
Edition number: 1st ed. 2022
Publisher: Springer
Date of Publication: 12 February 2023
Number of Volumes: 1 pieces, Book
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Short description:
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 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.
Long description:
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 is a book on the representation theory of p-adic groups on p-adic Banach spaces whose foundations were laid by Schneider and Teitelbaum. It explains their duality theory and demonstrates its applications to continuous principal series. ... It could also be of an interest to mathematicians who are working in the representation theory on complex vector spaces.? (Barbara Bošnjak, zbMATH 1523.22001, 2023)
This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
?This is a book on the representation theory of p-adic groups on p-adic Banach spaces whose foundations were laid by Schneider and Teitelbaum. It explains their duality theory and demonstrates its applications to continuous principal series. ... It could also be of an interest to mathematicians who are working in the representation theory on complex vector spaces.? (Barbara Bošnjak, zbMATH 1523.22001, 2023)
Table of Contents:
- 1. Introduction. - Part I Banach Space Representations of p-adic Lie Groups. - 2. Iwasawa Algebras. - 3. Distributions. - 4. Banach Space Representations. - Part II Principal Series Representations of Reductive Groups. - 5. Reductive Groups. - 6. Algebraic and Smooth Representations. - 7. Continuous Principal Series. - 8. Intertwining Operators.