Tables of Representations of Simple Lie Algebras, Volume I. Exceptional Simple Lie Algebras

V. 1. Exceptional Simple Lie Algebras. W.g. Mckay, J. Patera And D.w. Rand. Includes Bibliographical References (v. 1, Pages 325-327). Tables of Representations of Simple Lie Algebras Volume I. Exceptional Simple Lie Algebras, W. G. McKay, J. Patera, D. W. Rand, 1990, Les publications CRM, 2921120062 Copyright foreword contents chapter 1. Introduction to the Series chapter 2. Properties of Simple Lie Algebras and their Representations 2.1. Cartan matrix 2.2. Determinant of the Cartan Matrix 2.3. Coxeter-Dynkin Diagram 2.4. Roots 2.5. Fundamental Weights 2.6. The Highest Weight 2.7. Weight System of a Representation 2.8. Weights 2.9. Weyl Group Orbits 2.10. Multiplicities of Weights 2.11. Distinct Weight Algorithm 2.12. Distinct Dominant Weight Algorithm 2.13. Tensor Product of Representations 2.14. Semisimple and Reductive Nonsimple Lie Algebras 2.15. Weight Level 2.16. Congruence Class 2.17. Dimension 2.18. Second Index 2.19. Higher Indices 2.20. Orthogonal and Symplectic Representations 2.21. Maximal Reductive Subalgebras 2.22. Maximal Hypoalgebras of Simple Lie Algebras 2.23. Principal Three Dimensional Subalgebra chapter 3. Algorithm for Branching Rules 3.1. Subalgebras and Hypoalgebras 3.2. Tensor Products chapter 4. Comments to Volume I 4.1. Simple Lie Algebra E_6 4.2. Simple Lie Algebra E_7 4.3. Simple Lie Algebra E_8 4.4. Simple Lie Algebra F_4 4.5. Simple Lie Algebra G_2 chapter 5. Table 1 -- Biographies 5.1. About tlie Biographies Table Bios for A_n Bios for B_n Bios for C_n Bios for D_n Bios for E_6 Bios for E_7 Bios for E_8 Bios for F_4 Bios for G_2 chapter 6. Table 2 -- Irreducible Representations 6.1. About the Irreducible Representations Table Irreducible Representations of E_6 Irreducible Representations of E_7 Irreducible Representations of E_8 Irreducible Representations of F_4 Irreducible Representations of G_2 chapter 7. Table 3 -- Projection Matrices : Subalgebras 7.1. About the Projection Matrices Table Projection Matrices for Subalgebras of E_6 Projection Matrices for Subalgebras of E_7 Projection Matrices for Subalgebras of E_8 Projection Matrices for Subalgebras of F_4 Projection Matrices for Subalgebras of G_2 chapter 8. Table 4 -- Projection Matrices : Hypoalgebras 8.1. About the Projection Matrices Table Projection Matrices for Hypoalgebras of E_6, E_7, E_8, F_4, G_2 chapter 9. Table 5 -- Branching Rules : Subalgebras 9.1 About the Branching Rule Table 9.2 General Structure of Branching Rule Tables Branching Rules for E_6 Branching Rules for E_7 Branching Rules for E_8 Branching Rules for F_4 Branching Rules for G_2 chapter 10. Table 6 -- Branching Rules : Hypoalgebras 10.1 About the Branching Rule Table Branching Rules for E_6 Branching Rules for E_7 Branching Rules for E_8 Branching Rules for F_4 Branching Rules for G_2 chapter 11. Table 7 -- Tensor Product Decompositions 11.1 About the Tensor Product Decompositions Table Tensor Products for E_6 Tensor Products for E_7 Tensor Products for E_8 Tensor Products for F_4 Tensor Products for G_2 chapter 12. ABOUT simpLie references