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Tables of Contents for The Classical and Quantum 6J-Symbols
Chapter/Section Title
Page #
Page Count
Foreword
ix
Introduction
3
4
Representations of U(sl(2))
7
60
Basic definitions
7
1
Finite dimensional irreducible representations
7
5
Diagrammatics of U (sl(2)) invariant maps
12
3
The Temperley-Lieb algebra
15
6
Tensor Products of irreducible representations
21
6
The 6j-symbols
27
16
Computations
43
20
A recursion formula for the 6j-symbols
63
2
Remarks
65
2
Quantum sl(2)
67
60
Some finite dimensional representations
67
3
Representations of the braid groups
70
4
A finite dimensional quotient of C[B(n)]
74
3
A model for the representations VjA
77
3
The Jones-Wentzl projectors
80
13
The quantum Clebsch-Gordan theory
93
6
Quantum network evaluation
99
7
The quantum 6j-symbols--generic case
106
4
Diagrammatics of weight vectors (quantum case)
110
1
Twisting rules
111
12
Symmetries
123
2
Further identities among the quantum 6j-symbols
125
2
The Quantum Trace and Color Representations
127
24
The quantum trace
127
3
A bilinear form on tangle diagrams
130
3
Color representations
133
6
The quantum 6j-symbol--root of unity case
139
12
The Turaev-Viro Invariant
151
9
The definition of the Turaev-Viro invariant
151
6
Epilogue
157
3
References
160