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by James E. Humphreys
Download Representations of Semisimple Lie Algebras in the BGG Category $mathscr {O}$ (Graduate Studies in Mathematics) fb2
Mathematics
  • Author:
    James E. Humphreys
  • ISBN:
    0821846787
  • ISBN13:
    978-0821846780
  • Genre:
  • Publisher:
    American Mathematical Society (July 22, 2008)
  • Pages:
    289 pages
  • Subcategory:
    Mathematics
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    1969 kb
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Introduction to Lie Algebras and Representation Theory (Graduate Texts in. .See and discover other items: category theory.

Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics) (v. 9). Algebraic Geometry (Graduate Texts in Mathematics). Representation Theory: A First Course (Graduate Texts in Mathematics). Series: Graduate Studies in Mathematics (Book 94). Hardcover: 289 pages. Publisher: American Mathematical Society (July 22, 2008).

Graduate Studies in Mathematics Volume: 94; 2008; 289 pp; Hardcover MSC .

One of the goals Humphreys had in mind was to provide a textbook suitable for graduate students. This has been achieved by keeping prerequisites to a minimum, by careful dealing with technical parts of the proofs, and by offering a large number of exercises. Representations of Semisimple Lie Algebras in the BGG Category $mathscr{O}$.

Goodreads helps you keep track of books you want to read Part I can be used as a text for independent study or for a mid-level one semester graduate course.

Goodreads helps you keep track of books you want to read. Start by marking Representations of Semisimple Lie Algebras in the Bgg Category O as Want to Read: Want to Read savin. ant to Read. Part I can be used as a text for independent study or for a mid-level one semester graduate course.

Graduate Studies in Mathematics (GSM) is a series of graduate-level . 94 Representations of Semisimple Lie Algebras in the BGG Category .

Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). These books elaborate on several theories from notable personas, such as Martin Schechter and Terence Tao, in the mathematical industry. The books in this series are published only in hardcover. 94 Representations of Semisimple Lie Algebras in the BGG Category O, James E. Humphreys (2008, ISBN 978-0-8218-4678-0). 95 Quantum Mechanics for Mathematicians, Leon A. Takhtajan (2008

Representations of Semisimple Lie Algebras in the BGG Category O. Humphreys .

Representations of Semisimple Lie Algebras in the BGG Category O. Download (pdf, . 1 Mb) Donate Read. Epub FB2 mobi txt RTF. Converted file can differ from the original. If possible, download the file in its original format.

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oceedings{ntationsOS, title {Representations of Semisimple Lie Algebras in the Bgg Category O}, author {James E. Humphreys}, year {2008} }. James E.

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

E. Humphreys, Representations of Semisimple Lie Algebras in the BGG Category O, Graduate Studies in Mathematics 94 (American Mathematical Society, 2008). R. W. Carter, Lie algebras of finite and affine type (Cambridge University Press, 2005). D. Gaitsgory, Geometric representation theory, lecture notes (Harvard University, 2005). edu/~gaitsgde/267y/catO.

Publisher: American Mathematical Society. Graduate Studies in Mathematics 94. Price: 5. 0. ISBN: 978-0-8218-4678-0. Publication Date: 2008. See the table of contents in pdf format.

James E. Humphreys is presently Professor of Mathematics at the University of Massachusetts at Amherst. This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. Before this, he held the posts of Assistant Professor of Mathematics at the University of Oregon and Associate Professor of Mathematics at New York University.

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 $mathfrak{g}$ over $mathbb {C}$. The setting is the module category $mathscr {O}$ introduced by Bernstein-Gelfand-Gelfand, which includes all highest weight modules for $mathfrak{g}$ 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 $mathfrak{g}$. Basic techniques in category $mathscr {O}$ 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: $D$-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category $mathscr {O}$, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson-Ginzburg-Soergel.