Contents
Chapter 1. Introduction 1
1. Introduction 1
Chapter 2. Generalized Whittaker functions and representation
theory of SU(2,2) 5
2. Definition of the generalized Whittaker functions 5
3. Structure theory for SU(2,2) and its Lie algebra 7
4. Representations of K 11
5. Irreducible 5C/(£)-modules 13
6. Explicit description of Whittaker functions 15
7. Radial part of the shift operators 23
Chapter 3. Generalized Whittaker functions for Pj principal series
representations 43
8. Generalized Whittaker functions for Pj-principal series 43
Chapter 4. Generalized Whittaker functions for the discrete series
representations 61
9. Generalized Whittaker functions for the discrete series
representations 61
10. Generalized Whittaker functions for the holomorphic discrete
series representations 63
11. Generalized Whittaker functions for the large discrete series
representations 65
12. Generalized Whittaker functions for the middle discrete
representations 85
13. Generalized Whittaker functions for the middle discrete
series associated with definite H^ 85
14. Generalized Whittaker functions for the middle discrete
series associated with indefinite H^ 99
Bibliography 115
Vll
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