Free PDF D-Modules, Perverse Sheaves, and Representation Theory (Progress in Mathematics), by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
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D-Modules, Perverse Sheaves, and Representation Theory (Progress in Mathematics), by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
Free PDF D-Modules, Perverse Sheaves, and Representation Theory (Progress in Mathematics), by Ryoshi Hotta, Kiyoshi Takeuchi, Toshiyuki Tanisaki
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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.
- Sales Rank: #612479 in Books
- Brand: Brand: Birkhäuser
- Published on: 2007-11-07
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .94" w x 6.14" l, 1.70 pounds
- Binding: Hardcover
- 412 pages
- Used Book in Good Condition
Review
From the reviews:
"A self-contained introduction to D-modules, with the aim of showing how they were used to solve the Kazhdan-Lusztig conjecture. … present book can be used as a good reference on D-modules and on advanced representation theory of semisimple Lie algebras, but especially as a detailed account on the relations between them; in fact, in our opinion this is the first and very welcome complete work devoted to a mainstream research field (the ‘Algebraic Analysis’ approach to representation theory) which remains very active almost thirty years." (Corrado Marastoni, Mathematical Reviews, Issue 2008 k)
“The present book provides a reader-friendly treatment of the subject, suitable for graduate students who wish to enter the area. Part I of the book presents the theory of D-modules … . The treatment in the book is quite complete … . Part II provides the necessary background in the structure of semi-simple Lie algebras and their representations.” (Dennis Gaitsgory, Bulletin of the American Mathematical Society, Vol. 47 (4), October, 2010)
From the Back Cover
D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, 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. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory.
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, and representation theory.
Most helpful customer reviews
2 of 2 people found the following review helpful.
Fabulous
By Michael C. Berg
This book, on a pretty austere but exceedingly important subject (particulalry given the power and impact of the Riemann-Hilbert Correspondence) is a wonderful resource --- in fact, the book gives a full proof of "Riemann-Hilbert"!Additionally, the authors discuss a beautiful and deep connection to representation theory, which is not present in other texts. This makes the book particularly useful to people seeking to apply this material to other areas.
Finally, the book is very well written and accessible, provided of course that the reader has the required background (Recommendation: first study Kashiwara-Shapira's "Sheaves on Manifolds.").
0 of 0 people found the following review helpful.
Five Stars
By Ruifang Song
Excellent book!
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