p-adic Banach Space Representations

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.

Provides numerous exercises for graduate students and readers interested in hands-on learning Offers a comprehensive introduction to the representation theory of p-adic groups on p-adic Banach spaces Presents thoroughly the foundations and the Schneider-Teitelbaum duality

Autorentext

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.

Klappentext

• 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.

  Inhalt

  • 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.