Algorithms for Computations in Local Symmetric Spaces
Algorithms for Computations in Local Symmetric Spaces

Author:

Publisher:

Published: 2003

Total Pages:

ISBN-13:

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In this thesis, we use finite semisimple Lie theory to compute the structure of a local symmetric space p and its corresponding symmetric space P. Helminck classifies the local symmetric spaces over algebraically closed fields in [Hel88]. Here I extend these first results and write algorithms that implement combinatorial methods to compute `"nice" bases, restricted root systems, multiplicities and restricted Weyl groups for these spaces.

Locally Mixed Symmetric Spaces
Locally Mixed Symmetric Spaces

Author: Bruce Hunt

Publisher: Springer Nature

Published: 2021-09-04

Total Pages: 622

ISBN-13: 3030698041

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What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Representation Theory and Harmonic Analysis on Symmetric Spaces
Representation Theory and Harmonic Analysis on Symmetric Spaces

Author: Jens Gerlach Christensen

Publisher: American Mathematical Soc.

Published: 2018-08-27

Total Pages: 330

ISBN-13: 1470440709

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This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.

Asymptotically Symmetric Einstein Metrics
Asymptotically Symmetric Einstein Metrics

Author: Olivier Biquard

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 116

ISBN-13: 9780821831663

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The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence betweenEinstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods toconstruct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.

Lie Groups and Symmetric Spaces
Lie Groups and Symmetric Spaces

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 372

ISBN-13: 9780821834725

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The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927-2000). Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as thearticle by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest. The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.