D Modules Perverse Sheaves And Representation Theory

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D-Modules, Perverse Sheaves, and Representation Theory

Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki
D Modules Perverse Sheaves and Representation Theory Book PDF

Author : Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 54,6 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 9780817645236

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D-Modules, Perverse Sheaves, and Representation Theory by Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki Pdf

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.

Perverse Sheaves and Applications to Representation Theory

Pramod N. Achar
Perverse Sheaves and Applications to Representation Theory Book PDF

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 40,6 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

Algebraic D-modules

Armand Borel
Algebraic D modules Book PDF

Author : Armand Borel
Publisher : Unknown
Page : 382 pages
File Size : 40,9 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:49015000393570

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Algebraic D-modules by Armand Borel Pdf

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.

Sheaves in Topology

Alexandru Dimca
Sheaves in Topology Book PDF

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642188688

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Sheaves in Topology by Alexandru Dimca Pdf

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.

Representation Theory and Complex Geometry

Neil Chriss
Representation Theory and Complex Geometry Book PDF

Author : Neil Chriss
Publisher : Birkhauser
Page : 495 pages
File Size : 44,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780817637927

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Representation Theory and Complex Geometry by Neil Chriss Pdf

This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.

Lectures on Formal and Rigid Geometry

Siegfried Bosch
Lectures on Formal and Rigid Geometry Book PDF

Author : Siegfried Bosch
Publisher : Springer
Page : 254 pages
File Size : 45,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783319044170

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Lectures on Formal and Rigid Geometry by Siegfried Bosch Pdf

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

Representations of Semisimple Lie Algebras in the BGG Category O

James E. Humphreys
Representations of Semisimple Lie Algebras in the BGG Category O Book PDF

Author : James E. Humphreys
Publisher : American Mathematical Soc.
Page : 289 pages
File Size : 51,8 Mb
Release : 2021-07-14
Category : Education
ISBN : 9781470463267

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Representations of Semisimple Lie Algebras in the BGG Category O by James E. Humphreys Pdf

This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.

Categories and Sheaves

Masaki Kashiwara,Pierre Schapira
Categories and Sheaves Book PDF

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 40,8 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9783540279501

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Categories and Sheaves by Masaki Kashiwara,Pierre Schapira Pdf

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Mixed Twistor D-modules

Takuro Mochizuki
Mixed Twistor D modules Book PDF

Author : Takuro Mochizuki
Publisher : Springer
Page : 487 pages
File Size : 41,5 Mb
Release : 2015-08-19
Category : Mathematics
ISBN : 9783319100883

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Mixed Twistor D-modules by Takuro Mochizuki Pdf

We introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.

Modern Trends in Algebra and Representation Theory

David Jordan,Nadia Mazza,Sibylle Schroll
Modern Trends in Algebra and Representation Theory Book PDF

Author : David Jordan,Nadia Mazza,Sibylle Schroll
Publisher : Cambridge University Press
Page : 408 pages
File Size : 41,5 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781009103473

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Modern Trends in Algebra and Representation Theory by David Jordan,Nadia Mazza,Sibylle Schroll Pdf

Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Regular and Irregular Holonomic D-Modules

Masaki Kashiwara,Pierre Schapira
Regular and Irregular Holonomic D Modules Book PDF

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Cambridge University Press
Page : 119 pages
File Size : 42,9 Mb
Release : 2016-05-26
Category : Mathematics
ISBN : 9781316613450

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Regular and Irregular Holonomic D-Modules by Masaki Kashiwara,Pierre Schapira Pdf

A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.

Representation Theory and Algebraic Geometry

Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Representation Theory and Algebraic Geometry Book PDF

Author : Vladimir Baranovsky,Nicolas Guay,Travis Schedler
Publisher : Birkhäuser
Page : 0 pages
File Size : 50,5 Mb
Release : 2023-06-17
Category : Mathematics
ISBN : 3030820092

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Representation Theory and Algebraic Geometry by Vladimir Baranovsky,Nicolas Guay,Travis Schedler Pdf

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theory D-modules and perverse sheaves Analogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.

Nonlinear Analysis and its Applications to Differential Equations

M.R. Grossinho,M. Ramos,C. Rebelo,L. Sanchez
Nonlinear Analysis and its Applications to Differential Equations Book PDF

Author : M.R. Grossinho,M. Ramos,C. Rebelo,L. Sanchez
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 41,8 Mb
Release : 2000-11-29
Category : Mathematics
ISBN : 0817641882

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Nonlinear Analysis and its Applications to Differential Equations by M.R. Grossinho,M. Ramos,C. Rebelo,L. Sanchez Pdf

In this book we present a significant part ofthe material given in an autumn school on "Nonlinear Analysis and Differential Equations," held at the CMAF (Centro de Matematica e Aplica

Variational Theories for Liquid Crystals

E.G. Virga
Variational Theories for Liquid Crystals Book PDF

Author : E.G. Virga
Publisher : CRC Press
Page : 398 pages
File Size : 52,8 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351405652

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Variational Theories for Liquid Crystals by E.G. Virga Pdf

Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.

Sheaves on Manifolds

Masaki Kashiwara,Pierre Schapira
Sheaves on Manifolds Book PDF

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 44,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662026618

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Sheaves on Manifolds by Masaki Kashiwara,Pierre Schapira Pdf

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.