Displaying similar documents to “On the infinite fern of Galois representations of unitary type”

Dual Blobs and Plancherel Formulas

Ju-Lee Kim (2004)

Bulletin de la Société Mathématique de France

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Let k be a p -adic field. Let G be the group of k -rational points of a connected reductive group 𝖦 defined over k , and let 𝔤 be its Lie algebra. Under certain hypotheses on 𝖦 and k , wethe tempered dual G ^ of G via the Plancherel formula on 𝔤 , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on 𝔤 and G . As a consequence, we prove that any tempered representation contains a good minimal 𝖪 -type; we extend this result to irreducible...

Irreducibility of automorphic Galois representations of G L ( n ) , n at most 5

Frank Calegari, Toby Gee (2013)

Annales de l’institut Fourier

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Let π be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL n ( 𝔸 F ) , where F is a totally real field and n is at most 5 . We show that for all primes l , the l -adic Galois representations associated to π are irreducible, and for all but finitely many primes l , the mod l Galois representations associated to π are also irreducible. We also show that the Lie algebras of the Zariski closures of the l -adic representations are independent of l .

On critical values of twisted Artin L -functions

Peng-Jie Wong (2017)

Czechoslovak Mathematical Journal

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We give a simple proof that critical values of any Artin L -function attached to a representation ρ with character χ ρ are stable under twisting by a totally even character χ , up to the dim ρ -th power of the Gauss sum related to χ and an element in the field generated by the values of χ ρ and χ over ℚ . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.

ℒ -invariants and Darmon cycles attached to modular forms

Victor Rotger, Marco Adamo Seveso (2012)

Journal of the European Mathematical Society

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Let f be a modular eigenform of even weight k ≥ 2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D f F M and an ℒ -invariant ℒ f F M . The first goal of this paper is building a suitable p -adic integration theory that allows us to construct a new monodromy module D f and ℒ -invariant ℒ f , in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two ℒ -invariants...

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

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We consider the equation - y ' ( x ) + q ( x ) y ( x - ϕ ( x ) ) = f ( x ) , x ∈ ℝ , where ϕ and q ( q ≥ 1 ) are positive continuous functions for all x ∈ ℝ and f ∈ C ( ℝ ) . By a solution of the equation we mean any function y , continuously differentiable everywhere in ℝ , which satisfies the equation for all x ∈ ℝ . We show that under certain additional conditions on the functions ϕ and q , the above equation has a unique solution y , satisfying the inequality ∥ y ' ∥ C ( ℝ ) + ∥ q y ∥ C ( ℝ ) ≤ c ∥ f ∥ C ( ℝ ) , where the constant c ∈ ( 0 , ∞ ) does not depend on the choice of f .

Locally analytic vectors of unitary principal series of  GL 2 ( ℚ p )

Ruochuan Liu, Bingyong Xie, Yuancao Zhang (2012)

Annales scientifiques de l'École Normale Supérieure

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The p -adic local Langlands correspondence for  GL 2 ( ℚ p ) attaches to any 2 -dimensional irreducible p -adic representation V of  G ℚ p an admissible unitary representation Π ( V ) of  GL 2 ( ℚ p ) . The unitary principal series of  GL 2 ( ℚ p ) are those Π ( V ) corresponding to trianguline representations. In this article, for  p > 2 , using the machinery of Colmez, we determine the space of locally analytic vectors Π ( V ) an for all non-exceptional unitary principal series Π ( V ) of  GL 2 ( ℚ p ) by proving a conjecture of Emerton.