D Modules Perverse Sheaves And Representation Theory

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D-Modules, Perverse Sheaves, and Representation Theory

Author : Ryoshi Hotta
Publisher : Springer Science & Business Media
ISBN 13 : 081764363X
Total Pages : 408 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Ryoshi Hotta

Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta and published by Springer Science & Business Media. This book was released on 2007-11-07 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Perverse Sheaves, and Representation Theory

Author : Kiyoshi Takeuchi
Publisher : Springer Science & Business Media
ISBN 13 : 0817645233
Total Pages : 412 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Kiyoshi Takeuchi

Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Kiyoshi Takeuchi and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
ISBN 13 : 1470455978
Total Pages : 562 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar

Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 382 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Algebraic D-modules by : Armand Borel

Download or read book Algebraic D-modules written by Armand Borel and published by . This book was released on 1987 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
ISBN 13 : 3642188680
Total Pages : 240 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Sheaves in Topology by : Alexandru Dimca

Download or read book Sheaves in Topology written by Alexandru Dimca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Semisimple Lie Algebras in the BGG Category O

Author : James E. Humphreys
Publisher : American Mathematical Soc.
ISBN 13 : 1470463261
Total Pages : 289 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Semisimple Lie Algebras in the BGG Category O by : James E. Humphreys

Download or read book Representations of Semisimple Lie Algebras in the BGG Category O written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 2021-07-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Formal and Rigid Geometry

Author : Siegfried Bosch
Publisher : Springer
ISBN 13 : 3319044176
Total Pages : 254 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Lectures on Formal and Rigid Geometry by : Siegfried Bosch

Download or read book Lectures on Formal and Rigid Geometry written by Siegfried Bosch and published by Springer. This book was released on 2014-08-22 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".

Multiple Dirichlet Series, L-functions and Automorphic Forms

Author : Daniel Bump
Publisher : Springer
ISBN 13 : 0817683348
Total Pages : 361 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Multiple Dirichlet Series, L-functions and Automorphic Forms by : Daniel Bump

Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

Representation Theory and Complex Geometry

Author : Neil Chriss
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Representation Theory and Complex Geometry by : Neil Chriss

Download or read book Representation Theory and Complex Geometry written by Neil Chriss and published by . This book was released on 1997 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an attempt to provide an overview of some of the recent advances in representation theory from a geometric standpoint. A geometrically-oriented treatment is very timely and has long been desired, especially since the discovery of D-modules in the early '80s and the quiver approach to quantum groups in the early '90s.

The Geometry of Complex Domains

Author : Robert E. Greene
Publisher : Springer Science & Business Media
ISBN 13 : 0817646221
Total Pages : 303 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Geometry of Complex Domains by : Robert E. Greene

Download or read book The Geometry of Complex Domains written by Robert E. Greene and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.

The Geometry of Moduli Spaces of Sheaves

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Principles of Fuel Cells

Author : Xianguo Li
Publisher : CRC Press
ISBN 13 : 113520179X
Total Pages : 339 pages
Book Rating : 4.1/5 (352 download)

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Book Synopsis Principles of Fuel Cells by : Xianguo Li

Download or read book Principles of Fuel Cells written by Xianguo Li and published by CRC Press. This book was released on 2005-12-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is engineering oriented and covers a large variety of topics ranging from fundamental principles to performance evaluation and applications. It is written systematically and completely on the subject with a summary of state-of-the-art fuel cell technology, filling the need for a timely resource. This is a unique book serving academic researchers, engineers, as well as people working in the fuel cell industry. It is also of substantial interest to students, engineers, and scientists in mechanical engineering, chemistry and chemical engineering, electrochemistry, materials science and engineering, power generation and propulsion systems, and automobile engineering.

Categories and Sheaves

Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 3540279504
Total Pages : 498 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Categories and Sheaves by : Masaki Kashiwara

Download or read book Categories and Sheaves written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Categorical Foundations

Author : Maria Cristina Pedicchio
Publisher : Cambridge University Press
ISBN 13 : 9780521834148
Total Pages : 452 pages
Book Rating : 4.8/5 (341 download)

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Book Synopsis Categorical Foundations by : Maria Cristina Pedicchio

Download or read book Categorical Foundations written by Maria Cristina Pedicchio and published by Cambridge University Press. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 9780521801973
Total Pages : 302 pages
Book Rating : 4.8/5 (19 download)

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Book Synopsis Topics in Algebraic Graph Theory by : Lowell W. Beineke

Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.

Oriented Matroids

Author : Anders Björner
Publisher : Cambridge University Press
ISBN 13 : 052177750X
Total Pages : 564 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Oriented Matroids by : Anders Björner

Download or read book Oriented Matroids written by Anders Björner and published by Cambridge University Press. This book was released on 1999-11-18 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Etale Cohomology (PMS-33)

Author : J. S. Milne
Publisher : Princeton University Press
ISBN 13 : 9780691082387
Total Pages : 346 pages
Book Rating : 4.0/5 (823 download)

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Book Synopsis Etale Cohomology (PMS-33) by : J. S. Milne

Download or read book Etale Cohomology (PMS-33) written by J. S. Milne and published by Princeton University Press. This book was released on 1980-04-21 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. 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.