Roberts B.K., Schmidt R. — Local Newforms for GSp(4) :: Электронная библиотека попечительского совета мехмата МГУ

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Roberts B.K., Schmidt R. — Local Newforms for GSp(4)

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Название: Local Newforms for GSp(4)

Авторы: Roberts B.K., Schmidt R.

Аннотация:

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 315

Добавлена в каталог: 13.05.2008

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Предметный указатель

-filtration, table      277 279
-theory      66
-theory and paramodular vectors      117
$\eta$ Principle      125 136 146
$\gamma$ -factor      81
$\varepsilon$ -factors, degree 4 table      284
$\varepsilon$ -factors, degree 5 table      289
$\varepsilon$ -factors, for representations of       60
$\varepsilon$ -factors, of generic representations      265
$\varepsilon$ -factors, via zeta integrals      82
Atkin — Lehner eigenvalues      183
Atkin — Lehner eigenvalues for oldforms      186
Atkin — Lehner eigenvalues in Iwahori-spherical representations      105 293
Atkin — Lehner eigenvalues in Saito — Kurokawa representations      176
Atkin — Lehner eigenvalues, table      291
Atkin — Lehner element      31
Based root datum      41
Borel subgroup      28 41
Casselman — Shalika formula      243
CHARACTER      33
Component group      48
Conductor of a character      28
Conductor of a representation of       60
Contragredient      33 34
Coroots      41
Coset representatives for double cosets      153
Coset representatives for Hecke operators      189 190 192
Coset representatives, GSp(4, o) and Siegel      152
Coset representatives, Klingen      108
Coset representatives, paramodular      92 109
Coset representatives, paramodular - Klingen      107
Degenerate paramodular vectors      125
Double cosets      153
Double cosets, formula for Hecke operators      188
Dual group      41
Dual Hecke operators      193
Dual parabolic subgroup      41
EXPONENT      38 271
Frobenius reciprocity      33
Functional equation      81
Generic main theorem      264
Generic oldforms theorem      265
GSp(4) and SO(5)      286
Hecke algebra      188
Hecke algebra for the paramodular group      188
Hecke eigenvalues      263
Hecke eigenvalues and L-functions      264
Hecke eigenvalues for unramified representations      239
Hecke eigenvalues in Klingen induced representations      231
Hecke eigenvalues in Siegel induced representations      215
Hecke eigenvalues, table      294
Hecke operators and level raising      206
Hecke operators and twisting      194
Hecke operators for GL(2)      214
Hecke operators for the paramodular group      188
Hecke operators in unitary representations      236
Hecke operators, commutation relation      196
Hecke operators, diagonalizability      237
Hecke operators, dual      193
Irreducible constituent      33
Irreducible constituents for groups IV, V and VI      38
Irreducible subquotient, same as irreducible constituent      33
Iwahori factorization      32
Iwahori-spherical representations      105
Iwahori-spherical representations, table      293
Jacobi subgroup      29
Jacquet modules      33
Jacquet modules, table (Klingencase)      275
Jacquet modules, table (Siegelcase)      273
Kirillov model      62
Klingen congruence subgroup      32
Klingen congruence subgroup, cosets      107 108
Klingen congruence subgroup, volume      108
Klingen induced representations      166
Klingen parabolic subgroup      29
Klingen vectors and $\theta'$       126
L-function, degree 4 table      283
L-function, degree 5 table      288
L-function, for representations of       60
L-function, via zeta integrals      81
L-parameter      48
L-parameter and non-supercuspidal newforms      267
L-parameter, list for non-supercuspidal representations      52
L-parameter, table      281
Level lowering operators      107
Level lowering operators and level raising operators      116
Level lowering operators, explicit formulas      111 113 114
Level of a GL(2, F) representation      157
Level raising operators      91
Level raising operators, and Hecke operators      206
Level raising operators, and level lowering operators      116
Level raising operators, and zeta integrals      125
Level raising operators, commutativity      95
Level raising operators, explicit formulas      93

Level raising operators, injectivity      103
Linear independence of paramodular vectors      89
Local Langlands correspondence      48
Local Langlands correspondence, desiderata      49
Local Langlands correspondence, table      281
Main Theorem      264
Modular character      33
Multiplier      28
Newforms      95 262
Newforms, and L- and $\varepsilon$ -factors, generic case      264 265
Newforms, and L- and $\varepsilon$ -factors, non-supercuspidal case      267
Newforms, Hecke eigenvalues of      263
Newforms, Hecke eigenvalues of, table      294
Newforms, uniqueness      262
Oldforms      95
Oldforms Principle      95 182 266
Oldforms Principle for generic representations      265
Oldforms Principle for Saito — Kurokawa representations      176
Oldforms Principle for type IIIb      164
Oldforms Principle for type IVb      180
Oldforms Principle for type VId      180
Parabolic induction      35
Parabolic induction and paramodular vectors, Klingen case      166
Parabolic induction and paramodular vectors, Siegel case      159
Paramodular group      31
Paramodular group, cosets      92 107 109
Paramodular group, volume      108
Paramodular vectors      86
Paramodular vectors and -theory      117
Paramodular vectors in Saito — Kurokawa representations      175
Paramodular vectors, degenerate      125
Paramodular vectors, dimensions are non-decreasing      106
Paramodular vectors, dimensions, table      291
Paramodular vectors, existence      148
Paramodular vectors, linear independence      89
Paramodular vectors, lower bound on dimensions      147
Paramodular vectors, non-existence      120
Paramodular vectors, non-vanishing on diagonal      147
Paramodular vectors, support of      124
Paramodular vectors, zeta integrals of      123
Poles and -theory      128
R operator      248
Recursion formulas      245 255 259
Representation      33
Representation of the Weil — Deligne group      47
Representation, admissible      33
Representation, generic      34
Representation, induced      33
Representation, irreducible      33
Representation, smooth      33
Representation, smooth of       63
Representation, table of non-supercuspidals      270
Representation, tempered      266
Representation, trivial      33
Representation, twisted      36
Representation, unitary      33 236
Representation, unitary, table      271
Root datum      41
Saito — Kurokawa representations      170
Saito — Kurokawa representations, characterization of      180
Shadow vector      261
Siegel congruence subgroup      31 151
Siegel induced representations      159
Siegel parabolic subgroup      29
Simplified zeta integral      123
Steinberg representation      38
Theta injectivity      103 106
Theta injectivity, counterexample      106
Twisting      36
Twisting and Hecke operators      194
Twisting, representation invariant under      106
Twisting, representations of       47
Uniqueness at the minimal level      262
Uniqueness at the minimal level, non-supercuspidal case      182
Unitary representations (table)      271
Useful identity      34
Volumes of Klingen and paramodular subgroups      108
Weil group      46
Weil — Deligne group      47
Weyl group      30
Whittaker model      34
Zeta integral ideal      78
Zeta integrals      76
Zeta integrals of paramodular vectors      123
Zeta integrals of the newform      264
Zeta integrals of the newform, higher level case      259
Zeta integrals of the newform, level p case      247
Zeta integrals of the newform, supercuspidal case      260
Zeta integrals of the newform, unramified case      242
Zeta integrals, and level raising operators      125
Zeta integrals, in terms of Hecke eigenvalues, higher level case      259
Zeta integrals, in terms of Hecke eigenvalues, level p case      246
Zeta integrals, in terms of Hecke eigenvalues, unramified case      241
Zeta polynomials      126

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