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D-Modules and Spherical Representations. (MN-39):, Bien Frederic V.


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Автор: Bien Frederic V.
Название:  D-Modules and Spherical Representations. (MN-39):
ISBN: 9780691608327
Издательство: Wiley
Классификация:



ISBN-10: 0691608326
Обложка/Формат: Paperback
Страницы: 142
Вес: 0.20 кг.
Дата издания: 14.07.2014
Серия: Princeton legacy library
Язык: English
Иллюстрации: Black & white illustrations
Размер: 234 x 156 x 8
Читательская аудитория: Tertiary education (us: college)
Ссылка на Издательство: Link
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Поставляется из: Англии
Описание:

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by functions on pseudo-Riemannian symmetric spaces, i.e., spherical representations. The problem is then to describe the spherical representations among all irreducible ones, and to compute their multiplicities. This is the goal of this work, achieved fairly completely at least for the discrete series representations of reductive symmetric spaces. The book provides a general introduction to the theory of D-modules on flag varieties, and it describes spherical D-modules in terms of a cohomological formula. Using microlocalization of representations, the author derives a criterion for irreducibility. The relation between multiplicities and singularities is also discussed at length.

Originally published in 1990.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.



Regular and Irregular Holonomic D-Modules

Автор: Kashiwara
Название: Regular and Irregular Holonomic D-Modules
ISBN: 1316613453 ISBN-13(EAN): 9781316613450
Издательство: Cambridge Academ
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Цена: 8395.00 р.
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Описание: The theory of D-modules applies to many areas, including linear PDEs, group representation, algebraic geometry and mathematical physics. This book is the first devoted specifically to the most important variety, holonomic D-modules. It provides a complete unified treatment of the theory of holonomic D-modules, both regular and irregular.

The Structure and Stability of Persistence Modules

Автор: Chazal
Название: The Structure and Stability of Persistence Modules
ISBN: 3319425439 ISBN-13(EAN): 9783319425436
Издательство: Springer
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Цена: 6986.00 р.
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Описание:

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.

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