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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.

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.

Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups

2017-07-13 Mathematics
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Release : 2017-07-13
Genre : Mathematics
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Book Rating : 620/5 ( reviews)

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Book Synopsis Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups by : Matthew J. Emerton

Download or read book Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups written by Matthew J. Emerton. This book was released on 2017-07-13. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

p-Adic Lie Groups

2011-06-11 Mathematics
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Release : 2011-06-11
Genre : Mathematics
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Book Rating : 47X/5 ( reviews)

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Book Synopsis p-Adic Lie Groups by : Peter Schneider

Download or read book p-Adic Lie Groups written by Peter Schneider. This book was released on 2011-06-11. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Around Langlands Correspondences

2017 Mathematics
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Release : 2017
Genre : Mathematics
Kind : eBook
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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