Induction automorphe pour <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="italic">GL</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">C</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>

Henniart, Guy

doi:10.1016/j.jfa.2009.12.013

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…The epsilon factor is again inductive in degree zero, so that if π and π are induced representations of Whittaker type of GL n (C) and AI C/R π and AI C/R π denote the induced representation of Whittaker type of GL 2n (R) obtained by induction [Hen10], then…”

Section: Theorem 415 (Cf Theorem 310) For An Induced Representation O...mentioning

confidence: 99%

Archimedean Newform Theory For

Humphries

2024

J. Inst. Math. Jussieu

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We introduce a new invariant, the conductor exponent, of a generic irreducible Casselman–Wallach representation of $\operatorname {\mathrm {GL}}_n(F)$ , where F is an archimedean local field, that quantifies the extent to which this representation may be ramified. We also determine a distinguished vector, the newform, occurring with multiplicity one in this representation, with the complexity of this vector measured in a natural way by the conductor exponent. Finally, we show that the newform is a test vector for $\operatorname {\mathrm {GL}}_n \times \operatorname {\mathrm {GL}}_n$ and $\operatorname {\mathrm {GL}}_n \times \operatorname {\mathrm {GL}}_{n - 1}$ Rankin–Selberg integrals when the second representation is unramified. This theory parallels an analogous nonarchimedean theory due to Jacquet, Piatetski-Shapiro, and Shalika; combined, this completes a global theory of newforms for automorphic representations of $\operatorname {\mathrm {GL}}_n$ over number fields. By-products of the proofs include new proofs of Stade’s formulæ and a new resolution of the test vector problem for archimedean Godement–Jacquet zeta integrals.

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Section: Theorem 415 (Cf Theorem 310) For An Induced Representation O...mentioning

confidence: 99%

Archimedean Newform Theory For

Humphries

2024

J. Inst. Math. Jussieu

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On the K-Theory of the Reduced $$C^*$$ C ∗ -Algebras of $$GL(n,\mathbb {R})$$ G L ( n , R ) and $$GL(n,\mathbb {C})$$ G L ( n , C )

Mendes

2017

Springer Proceedings in Mathematics &Amp; Statistics

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On representations distinguished by unitary groups

2012

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Let E/F be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on GL n (A E ) over a unitary group of a Hermitian form with respect to E/F. We provide factorization for these periods into locally defined functionals, express these factors in terms of suitably defined local periods and characterize global distinction. We also study in detail the analogous local question and analyze the space of invariant linear forms under a unitary group. CONTENTS

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Induction automorphe pour GL(n,C)

Cited by 6 publications

References 19 publications

Archimedean Newform Theory For

Archimedean Newform Theory For

On the K-Theory of the Reduced $$C^*$$ C ∗ -Algebras of $$GL(n,\mathbb {R})$$ G L ( n , R ) and $$GL(n,\mathbb {C})$$ G L ( n , C )

On representations distinguished by unitary groups

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