Representation Theory and Noncommutative Harmonic Analysis II

Representation Theory and Noncommutative Harmonic Analysis II
Title Representation Theory and Noncommutative Harmonic Analysis II PDF eBook
Author A.A. Kirillov
Publisher Springer Science & Business Media
Pages 274
Release 2013-03-09
Genre Mathematics
ISBN 3662097567

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Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Representation Theory and Analysis on Homogeneous Spaces

Representation Theory and Analysis on Homogeneous Spaces
Title Representation Theory and Analysis on Homogeneous Spaces PDF eBook
Author Semen Grigorʹevich Gindikin
Publisher American Mathematical Soc.
Pages 272
Release 1994
Genre Mathematics
ISBN 082180300X

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A combination of new results and surveys of recent work on representation theory and the harmonic analysis of real and p-adic groups. Among the topics are nilpotent homogeneous spaces, multiplicity formulas for induced representations, and new methods for constructing unitary representations of real reductive groups. The 12 papers are from a conference at Rutgers University, February 1993. No index. Annotation copyright by Book News, Inc., Portland, OR

Harmonic Analysis on Homogeneous Spaces

Harmonic Analysis on Homogeneous Spaces
Title Harmonic Analysis on Homogeneous Spaces PDF eBook
Author Nolan R. Wallach
Publisher Courier Dover Publications
Pages 386
Release 2018-12-18
Genre Mathematics
ISBN 0486816923

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This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.

Geometric and Harmonic Analysis on Homogeneous Spaces

Geometric and Harmonic Analysis on Homogeneous Spaces
Title Geometric and Harmonic Analysis on Homogeneous Spaces PDF eBook
Author Ali Baklouti
Publisher Springer Nature
Pages 227
Release 2019-08-31
Genre Mathematics
ISBN 3030265625

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This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.

Homogeneous Spaces and Equivariant Embeddings

Homogeneous Spaces and Equivariant Embeddings
Title Homogeneous Spaces and Equivariant Embeddings PDF eBook
Author D.A. Timashev
Publisher Springer
Pages 254
Release 2011-04-07
Genre Mathematics
ISBN 9783642183980

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Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of "combinatorial" nature (the Luna-Vust theory) and description of various geometric and representation-theoretic properties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress obtained in and around the theory of spherical varieties.

Algebraic and Analytic Methods in Representation Theory

Algebraic and Analytic Methods in Representation Theory
Title Algebraic and Analytic Methods in Representation Theory PDF eBook
Author
Publisher Elsevier
Pages 357
Release 1996-09-27
Genre Mathematics
ISBN 0080526950

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This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces
Title An Introduction to Lie Groups and the Geometry of Homogeneous Spaces PDF eBook
Author Andreas Arvanitogeōrgos
Publisher American Mathematical Soc.
Pages 162
Release 2003
Genre Homogeneous spaces
ISBN 0821827782

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It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.