The Unitary and Rotation Groups

Title Page......Page 1
Copyright Page......Page 2
Preface......Page 4
Contents......Page 5
1. The n-Dimensional Unitary and Rotation Groups......Page 6
2. The Parametrization of the n-Dimensional Unitary and Rotation Groups......Page 12
3. The Class and In-Class Parameters of the n-Dimensional Unitary Group......Page 19
4. The Class and In-Class Parameters of the n-Dimensional Rotation Group......Page 25
5. The Element of Volume of a Parameter Group......Page 32
6. The Characteristic Matrices of a Matrix Group......Page 38
7. The Adjoint Representation of the n-Dimensional Unitary Group.......Page 45
8. The Class Factor of the Element of Volume of the n-Dimensional Unitary and Rotation Groups......Page 52
9. Representations of the n-Dimensional Unitary and Rotation Groups......Page 60
10. The Orthogonality Relations for a Compact Parameter Group......Page 68
11. The Irreducible Representations of the n-Dimensional Unitary Group......Page 76
12. The Analysis of any Power of a Representation of the n-Dimensional Unitary Group......Page 85
13. The Spin Representations of the Proper, Time-Sense Preserving Lorentz Group and of the 3-Dimensional Rotation Group......Page 93
14. The Simple Characters of the n-Dimensional Rotation Group......Page 103
15. The Analysis of the Representations Tcw,> ?(a) of the 2-Dimensional Unimodular Unitary Group......Page 112
16. The Analysis of the Product of Irreducible Representations of the n-Dimensional Unitary Group......Page 124
17. The Modification Rules for the n-Dimensional Rotation Group......Page 134
18. The Analysis of the Representations r (p) ?(a) and r? 0 (X) of the n-Dimensional Unitary Group......Page 143
Bibliography......Page 152
Index......Page 154