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Item Details
| Title:
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REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS IN THE BGG CATEGORY O
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| By: |
James E. Humphreys |
| Format: |
Hardback |
| List price:
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£62.95 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821846787 |
| ISBN 13: |
9780821846780 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 July, 2008 |
| Edition: |
UK ed. |
| Series: |
Graduate Studies in Mathematics No. 94 |
| Pages: |
289 |
| Description: |
Discusses the Kazhdan-Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra $\mathfrak{g}$ over $\mathbb {C}$. This work covers topics including parabolic category $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors and Koszul duality theorem of Beilinson-Ginzburg-Soergel. |
| Synopsis: |
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. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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