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Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 June 2014

JACK A. THORNE
JACK A. THORNE*
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA; [email protected]

Abstract

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We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$. This gives a systematic way to construct irreducible Galois representations whose residual representation is reducible.

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 2 , 01 July 2014 , e16
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author 2014

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