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Parabolically Induced Banach Space Representation of P-adic Groups

2020 Banach spaces
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Release : 2020
Genre : Banach spaces
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Book Synopsis Parabolically Induced Banach Space Representation of P-adic Groups by : Chathurika Umayangani Athapattu

Download or read book Parabolically Induced Banach Space Representation of P-adic Groups written by Chathurika Umayangani Athapattu. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: Parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups. We study the parabolic induction for p-adic Banach space representation of p-adic groups. In this dissertation, using the Schneider-Teitelbaum duality, we consider the corresponding Iwasawa modules. We present the dual of parabolically induced representation in terms of the tensor product.

p-adic Banach Space Representations

2023-02-11 Mathematics
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Release : 2023-02-11
Genre : Mathematics
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Book Rating : 844/5 ( reviews)

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Book Synopsis p-adic Banach Space Representations by : Dubravka Ban

Download or read book p-adic Banach Space Representations written by Dubravka Ban. This book was released on 2023-02-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry and Representation Theory of Real and p-adic groups

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
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Book Rating : 626/5 ( reviews)

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Book Synopsis Geometry and Representation Theory of Real and p-adic groups by : Juan Tirao

Download or read book Geometry and Representation Theory of Real and p-adic groups written by Juan Tirao. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.

Around Langlands Correspondences

2017 Mathematics
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Release : 2017
Genre : Mathematics
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Book Rating : 73X/5 ( reviews)

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Book Synopsis Around Langlands Correspondences by : Farrell Brumley

Download or read book Around Langlands Correspondences written by Farrell Brumley. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.

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