Algebraic Theory Of D Modules

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Algebraic D Modules

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Author : Armand Borel
language : en
Publisher:
Release Date : 1987

Algebraic D Modules written by Armand Borel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.

A Primer Of Algebraic D Modules

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Author : S. C. Coutinho
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-07

A Primer Of Algebraic D Modules written by S. C. Coutinho and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-07 with Mathematics categories.

The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

Algebraic Theory Of D Modules

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Author : Joseph Bernstein
language : en
Publisher:
Release Date : 1984

Algebraic Theory Of D Modules written by Joseph Bernstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.

D Modules Perverse Sheaves And Representation Theory

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Author : Kiyoshi Takeuchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12

D Modules Perverse Sheaves And Representation Theory written by Kiyoshi Takeuchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-12 with Mathematics categories.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

D Modules And Microlocal Calculus

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Author : Masaki Kashiwara
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

D Modules And Microlocal Calculus written by Masaki Kashiwara and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.

Analytic D Modules And Applications

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Author : Jan-Erik Björk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Analytic D Modules And Applications written by Jan-Erik Björk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a large variety of results concerning microdifferential analysis. Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables. The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets. For graduate students and researchers.

Regular And Irregular Holonomic D Modules

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Author : Masaki Kashiwara
language : en
Publisher:
Release Date : 2016

Regular And Irregular Holonomic D Modules written by Masaki Kashiwara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with D-modules categories.

A Study In Derived Algebraic Geometry

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Author : Dennis Gaitsgory
language : en
Publisher: American Mathematical Society
Release Date : 2019-12-31

A Study In Derived Algebraic Geometry written by Dennis Gaitsgory and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-31 with Mathematics categories.

Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.

D Modules Representation Theory And Quantum Groups

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Author : Louis Boutet de Monvel
language : en
Publisher: Springer
Release Date : 2006-11-15

D Modules Representation Theory And Quantum Groups written by Louis Boutet de Monvel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.

D Modules And Spherical Representations Mn 39

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Author : Frédéric V. Bien
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14

D Modules And Spherical Representations Mn 39 written by Frédéric V. Bien and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.

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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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.