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Translation Functors and the Shapovalov Determinant

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Author(s): Emilie Wiesner
Series: PhD thesis at University of Wisconsin-Madison
Year: 2005

Language: English

0.1.
0.2.
Contents
Abstract
Introduction
Chapter 1. Basics and Background
1.1.
1.2.
1.3.
Some Definitions for Lie Algebras
Semisimple Lie Algebras
Odds and Ends
Chapter 2. Lie Algebras with Triangular Decomposition
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
The Category (9
Special Filtrations in Category (9
Blocks
The Contravariant Form and the Shapovalov Determinant
Jantzen Filtrations
Translation Functors
Chapter 3. The Virasoro Algebra
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
Category (9
Affine Lie Algebras
The Virasoro Algebra and Affine Lie Algebras
A Determinant Formula for M (A)
Blocks
Translation Functors
Chapter 4. Quantum Groups
ii
13
15
18
22
31
34
35
40
41
42
44
51
56
70
82
4.1. The Restricted Integral Form U253 (9)
4.2. A PBW Basis for Ufflg)
4.3. The Category 0
4.4. Embeddings of Verma Modules
4.5. The Shapovalov Determinant
4.6. Translation Functors
Bibliography
iii
84
85
86
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