P R E F A C E This paper r e p r e s e n t s a continuation of the p r o g r a m begun by L. Auslander and C. C. Moore in their book [5], Unfortunately, consideration s of space prohibit this paper fro m being self-contained. The following is a rough guide to p r e r e q u i s i t e s : (1) C h a p t e r s II a n d III a r e e s s e n t i a l l y s e l f - c o n t a i n e d (and h a v e l i t t l e t o do w i t h r e p r e s e n t a t i o n t h e o r y ) . (2) The remainin g chapter s a s s u m e a knowledge of unitar y r e p r e - sentation theory . The m o s t economica l sourc e for the facts we shall need is Sections 2 - 9 of Chapter I of [5]. Sections 1 - 2 of [20]. An alternativ e sourc e is the set of notes [19] by Mackey. F o r complete proofs , one good sourc e is [9]. Although helpful, a knowledge of [22] and [5] is not needed. (3) Some standar d facts about r e a l algebrai c groups a r e used throughout the late r c h a p t e r s . The needed facts a r e s u m m a r i z e d in the introductor y m a t e r i a l to [25]. Alternatively, one can consult section 1 of [1]. Chapter VII als o use s [17], pp. 31-43. During the preparatio n of this m a n u s c r i p t , the author was sup - porte d by a National Science Foundation Graduate Fellowship . Severa l people have been v e r y helpful to m e , and it is a pleasur e to be able to thank the m h e r e . Severa l conversation s with B . Kostant o v e r c a m e m y initial feeling that T h e o r e m VI. 5 was false in fact, it wa s thanks to Prof. Kostant' s outlining his geometri c inductive procedur e that the possibility of a proof for VI. 5 along the p r e s e n t lines o c c u r r e d to m e . J. Dixmier was kind enough to go through an e a r l i e r (and far rougher ) Receive d by the editor s October 4, 1967. l i
Previous Page Next Page