TABLE OF CONTENTS
ABSTRACT vi
LIST OF FIGURES vii
LIST OF TABLES viii
INTRODUCTION ix
Chapter
1. NOTATION AND PRELIMINARIES 1
1.1. SP2n(F) 1
1.2. Induced representations and Jacquet modules 4
2. THE HECKE ALGEBRA APPROACH 8
2.1. General theorems 8
2.2. Basis for VB* 14
2.3. Irreducibility when (order \u) 2 30
2.4. Irreducibility conditions for (order Xu) 2 34
2.5. Irreducibility conditions for (order Xu) = 1 45
2.6. Reducibility conditions for (order Xu) = 1 53
2.7. Reducibility conditions for (order Xu) 2 57
3. IRREDUCIBILITY OF CERTAIN REPRESENTATIONS A LA TADIC 59
3.1. A general theorem on reducibility/irreducibility (in the regular
case) 59
3.2. Applications to degenerate principal series for Sp2n(F) (in the
regular case) 63
4. IRREDUCIBILITY CRITERIA FOR DEGENERATE PRINCIPAL
SERIES IN SP4(F), SPe(F), A LA TADIC 70
4.1. Extending definitions to the nonregular case . 70
4.2. Degenerate Principal Series in 5p4(jF) 71
4.3. Degenerate Principal Series in Spe(F) 76
APPENDIX 104
REFERENCES 109
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