Local Newforms for GSp(4) Book

A Summary     1
Representation Theory     27
Definitions     27
Parabolically Induced Representations     34
Dual Groups     40
The Local Langlands Correspondence     46
P[subscript 3]-Theory     62
Zeta Integrals     74
Paramodular Vectors     85
Linear Independence     85
The Level Raising Operators [theta], [theta]' and [eta]     90
Level Lowering Operators     107
Paramodular Vectors and P[subscript 3]-Theory     117
Zeta Integrals     123
Paramodular Vectors and Zeta Integrals     123
Poles and P[subscript 3]-Theory     128
The [eta] Principle     135
The Existence Theorem for Generic Representations     148
Non-supercuspidal Representations     151
Double Coset Decompositions     151
Induction from the Siegel Parabolic Subgroup     156
Representations of Type IIIb and IVc     161
Induction from the Klingen Parabolic Subgroup     165
Saito-Kurokawa Representations     168
Summary     182
Atkin-Lehner Eigenvalues     183
Hecke Operators     187
Two Hecke Operators     188
The Commutation Relation     195
Hecke Operators and Level Raising     205
Computation of Hecke Eigenvalues     213
Some Consequences of Unitarity     236
Proofs of the Main Theorems     239
Zeta Integrals: The Unramified Case     239
Zeta Integrals: The Level p Case     243
The Operator R     248
Zeta Integrals: The Higher Level Case     252
Main Results     262
Tables for Representations of GSp(4)     269
Non-supercuspidal Representations     269
Unitary Representations     271
Jacquet Modules     273
The P[subscript 3]-Filtration     277
L-Parameters     280
L- and [epsilon]-factors (degree 4)     282
L- and [epsilon]-factors (degree 5)     286
Paramodular Dimensions and Atkin-Lehner Eigenvalues     290
Hecke Eigenvalues     294
Parahori-invariant Vectors     297
References     301
Index     305