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.
Ban
p-adic Banach Space Representations jetzt bestellen!
Weitere Infos & Material
- 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.
Dubravka Ban
received her doctoral degree at the University of Zagreb. She was a postdoctoral fellow at the International Centre for Theoretical Physics in Trieste and a visiting assistant professor at Purdue University. Ban was a Humboldt research fellow at the University of Münster and University of Bonn. Currently, she is a professor of mathematics at Southern Illinois University, Carbondale. Her research is in the representation theory of
p
-adic groups in the context of Langlands program. Trained in the smooth representations on complex vector spaces, she is intrigued by the
p
-adic Banach space representations and finds them very interesting objects to study.
