An explicit computation of $p$-stabilized vectors

Michitaka MIYAUCHI; Takuya YAMAUCHI

Displaying similar documents to “An explicit computation of $p$ -stabilized vectors”

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 $\hat{G}$ 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...

$ℒ$ -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 $k \geq 2$ 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...

2-Cohomology of semi-simple simply connected group-schemes over curves defined over $p$ -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $X$ be a proper, smooth, geometrically connected curve over a $p$ -adic field $k$ . Lichtenbaum proved that there exists a perfect duality: $Br (X) \times Pic (X) \to ℚ / ℤ$ between the Brauer and the Picard group of $X$ , from which he deduced the existence of an injection of $Br (X)$ in $\prod_{P \in X} Br (k_{P})$ where $P \in X$ and $k_{P}$ denotes the residual field of the point $P$ . The aim of this paper is to prove that if $G = \tilde{G}$ is an $X_{e t}$ - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results...

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

A localization property for $B_{p q}^{s}$ and $F_{p q}^{s}$ spaces

Hans Triebel (1994)

Studia Mathematica

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Let $f^{j} = \sum_{k} a_{k} f (2^{j + 1} x - 2 k)$ , where the sum is taken over the lattice of all points k in $ℝ^{n}$ having integer-valued components, j∈ℕ and $a_{k} \in ℂ$ . Let $A_{p q}^{s}$ be either $B_{p q}^{s}$ or $F_{p q}^{s}$ (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on $ℝ^{n} .$ The aim of the paper is to clarify under what conditions $∥ f^{j} | A_{p q}^{s} ∥$ is equivalent to $2^{j (s - n / p)} (\sum_{k} | a_{k} |^{p})^{1 / p} ∥ f | A_{p q}^{s} ∥$ .

Principalization algorithm via class group structure

Daniel C. Mayer (2014)

Journal de Théorie des Nombres de Bordeaux

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For an algebraic number field $K$ with $3$ -class group ${Cl}_{3} (K)$ of type $(3, 3)$ , the structure of the $3$ -class groups ${Cl}_{3} (N_{i})$ of the four unramified cyclic cubic extension fields $N_{i}$ , $1 \leq i \leq 4$ , of $K$ is calculated with the aid of presentations for the metabelian Galois group $G_{3}^{2} (K) = Gal (F_{3}^{2} (K) | K)$ of the second Hilbert $3$ -class field $F_{3}^{2} (K)$ of $K$ . In the case of a quadratic base field $K = ℚ (\sqrt{D})$ it is shown that the structure of the $3$ -class groups of the four $S_{3}$ -fields $N_{1}, ..., N_{4}$ frequently determines the type of principalization of the $3$ -class group of $K$ in $N_{1}, ..., N_{4}$ . This...

Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Robert Harron, Antonio Lei (2014)

Journal de Théorie des Nombres de Bordeaux

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Let $f$ be a cuspidal newform with complex multiplication (CM) and let $p$ be an odd prime at which $f$ is non-ordinary. We construct admissible $p$ -adic $L$ -functions for the symmetric powers of $f$ , thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus $p$ -adic $L$ -functions and prove an analogue of Pollack’s decomposition of the admissible...

On some imaginary triquadratic number fields $k$ with ${Cl}_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2021)

Commentationes Mathematicae Universitatis Carolinae

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Let $d$ be a square free integer and $L_{d} : = ℚ (ζ_{8}, \sqrt{d})$ . In the present work we determine all the fields $L_{d}$ such that the $2$ -class group, ${Cl}_{2} (L_{d})$ , of $L_{d}$ is of type $(2, 4)$ or $(2, 2, 2)$ .

On compactness and connectedness of the paratingent

Wojciech Zygmunt (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this note we shall prove that for a continuous function $ϕ : Δ \to ℝ^{n}$ , where $Δ \subset ℝ$ , the paratingent of $ϕ$ at $a \in Δ$ is a non-empty and compact set in $ℝ^{n}$ if and only if $ϕ$ satisfies Lipschitz condition in a neighbourhood of $a$ . Moreover, in this case the paratingent is a connected set.

$C^{*}$ -points vs $P$ -points and $P^{♭}$ -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

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In a Tychonoff space $X$ , the point $p \in X$ is called a $C^{*}$ -point if every real-valued continuous function on $C ∖ {p}$ can be extended continuously to $p$ . Every point in an extremally disconnected space is a $C^{*}$ -point. A classic example is the space $𝐖^{*} = ω_{1} + 1$ consisting of the countable ordinals together with $ω_{1}$ . The point $ω_{1}$ is known to be a $C^{*}$ -point as well as a $P$ -point. We supply a characterization of $C^{*}$ -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space...

The centralizer of a classical group and Bruhat-Tits buildings

Daniel Skodlerack (2013)

Annales de l’institut Fourier

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Let $G$ be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let $H$ be the centralizer of a semisimple rational Lie algebra element of $G .$ We prove that the Bruhat-Tits building $𝔅^{1} (H)$ of $H$ can be affinely and $G$ -equivariantly embedded in the Bruhat-Tits building $𝔅^{1} (G)$ of $G$ so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let $j$ and $j^{'}$ be maps from $𝔅^{1} (H)$ to $𝔅^{1} (G)$ which preserve the Moy–Prasad filtrations....

Generalized versions of Ilmanen lemma: Insertion of $C^{1, ω}$ or $C_{loc}^{1, ω}$ functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space $X$ , if $f_{1} : X \to ℝ$ is continuous and semiconvex with modulus $ω$ , $f_{2} : X \to ℝ$ is continuous and semiconcave with modulus $ω$ and $f_{1} \leq f_{2}$ , then there exists $f \in C^{1, ω} (X)$ such that $f_{1} \leq f \leq f_{2}$ . Using this result we prove a generalization of Ilmanen lemma (which deals with the case $ω (t) = t$ ) to the case of an arbitrary nontrivial modulus $ω$ . This generalization (where a $C_{l o c}^{1, ω}$ function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

$L_{p, q}$ spaces

Joseph Kupka

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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the $L_{p, q}$ spaces................................. 114. Integral representation of bounded linear functionals on $L_{p, q} (B)$ ........ 235. Examples in $L_{p, q}$ theory...................................................................................

On hereditary normality of $ω^{*}$ , Kunen points and character $ω_{1}$

Sergei Logunov (2021)

Commentationes Mathematicae Universitatis Carolinae

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We show that $ω^{*} ∖ {p}$ is not normal, if $p$ is a limit point of some countable subset of $ω^{*}$ , consisting of points of character $ω_{1}$ . Moreover, such a point $p$ is a Kunen point and a super Kunen point.

Displaying similar documents to “An explicit computation of p -stabilized vectors”

Displaying similar documents to “An explicit computation of $p$ -stabilized vectors”