Contents ix
2.2. The construction of unirreps 73
2.3. Restriction-induction functors 74
2.4. Generalized characters 74
2.5. Infinitesimal characters 75
2.6. Functional dimension 75
2.7. Plancherel measure 76
§3. Worked-out examples 77
3.1. The unitary dual 78
3.2. Construction of unirreps 80
3.3. Restriction functor 84
3.4. Induction functor 86
3.5. Decomposition of a tensor product of two unirreps 88
3.6. Generalized characters 89
3.7. Infinitesimal characters 91
3.8. Functional dimension 91
3.9. Plancherel measure 92
3.10. Other examples 93
§4. Proofs 95
4.1. Nilpotent groups with 1-dimensional center 95
4.2. The main induction procedure 98
4.3. The image of U(g) and the functional dimension 103
4.4. The existence of generalized characters 104
4.5. Homeomorphism of G and O(G) 106
Chapter 4. Solvable Lie Groups 109
§1. Exponential Lie groups 109
1.1. Generalities 109
1.2. Pukanszky condition 111
1.3. Restriction-induction functors 113
1.4. Generalized characters 113
1.5. Infinitesimal characters 117
§2. General solvable Lie groups 118
2.1. Tame and wild Lie groups 118
2.2. Tame solvable Lie groups 123
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