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I am deeply grateful to my thesis advisor, Prof. Victor Guillemin. Throughout my graduate studies at MIT, he has offered me constant guidance, support and encour-agement, both academically and non-academically. I could not thank him enough for the mathematics I learned from him as well as for all the care I got from him. I have been extremely lucky to have been able to work with him. I would like to thank Prof. David Vogan for the representation theory he taught me, and for the patience he had in answering all my questions. Every time I had problems of Lie theory, I could always go to his office. I would also like to thank Prof. Shlomo Sternberg and Prof. Zhengfang Zhou for the much-needed support I received from them. I have benefitted greatly from several talks with Prof. Bertram Kostant. I am also greatly indebted to Prof. Isadore Singer for two year research assistantship he offered me with DOE Grant DE-FG02-88ER25066, and again to Prof. Victor Guillemin, for one year research assistantship and the summer support. Many thanks to Phyllis Ruby, who has helped me in many different ways