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

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