Contents
Introduction 1
Acknowledgement 3
Lecture 1. The Classical Theory: Part I 5
Beginnings of representation theory1 13
Lecture 2. The Classical Theory: Part II 17
Lecture 3. Polarized Hodge Structures and Mumford-Tate Groups and
Domains 31
Lecture 4. Hodge Representations and Hodge Domains 51
Lecture 5. Discrete Series and n-Cohomology 69
Introduction 69
Appendix to Lecture 5: The Borel-Weil-Bott (BWB) theorem 91
Lecture 6. Geometry of Flag Domains: Part I 95
Appendix to Lecture 6: The GR- and KC- orbit structure of
ˇ
D and the
GR-orbit structure of U 120
Lecture 7. Geometry of Flag Domains: Part II 147
Appendix to Lecture 7: The Borel-Weil-Bott theorem revisited 161
Lecture 8. Penrose Transforms in the Two Main Examples 165
Appendix to Lecture 8: Proofs of the results on Penrose transforms for D
and D 178
Lecture 9. Automorphic Cohomology 191
Appendix I to Lecture 9: The K-types of the TDLDS for SU(2, 1)
and Sp(4) 209
Appendix II to Lecture 9: Schmid’s proof of the degeneracy of the HSSS
for TDLDS in the SU(2, 1) and Sp(4) cases 214
Appendix III to Lecture 9: A general result relating TDLDS and
Dolbeault cohomology of Mumford-Tate domains 218
Lecture 10. Miscellaneous Topics and Some Open Questions 221
Appendix to Lecture 10: Boundary components and Carayol’s result 245
Bibliography 299
Index 303
iii
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