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Representation Theory of Lie Algebras

Representation Theory of Lie Algebras

Representation Theory of Lie

Representation Theory of Lie Algebras Classification of Reductive Algebraic Groups Workshop on Group Theory 18 Dec 2006 - 5 Jan 2007, Bangalore Anupam Singh Chapter 1. Representations and Weyl’s Theorem 1 Chapter 2. Representations of sl(2) 3 2.1. Classification of sl(2)-modules 3 2.2. More Representations of sl(2) 5 2.3. Weyl Group Action on the Weights 6 Chapter 3. Root Space Decomposition 7 3.1. Special Linear Algebra A l , l ≥ 1 7 3.2. Orthogonal Algebra (odd dimension) B l , l ≥ 2 8 3.3. Symplectic Algebra C l , l ≥ 3 9 3.4. Orthogonal Algebra (even dimension) D l , l ≥ 4 10 Chapter 4. Representation Theory 13 4.1. Universal Enveloping Algebra 13 4.2. Abstract Theory of Weights 14 4.3. Weights and Maximal Vectors 15 4.4. Construction of L-modules 15 4.5. All finite dimensional Representations 16 Chapter 5. Some Representation of Classical Lie Algebras 19 5.1. Fundamental Representations of sl(n) 19 5.2. Fundamental Representations of so(n) 20 Bibliography 21 Contents i

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