Relative property (T) and linear groups

Talia Fernós

Displaying similar documents to “Relative property (T) and linear groups”

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

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Let $K$ be a global field of characteristic not 2. Let $Z = H ∖ G$ be a symmetric variety defined over $K$ and $S$ a finite set of places of $K$ . We obtain counting and equidistribution results for the S-integral points of $Z$ . Our results are effective when $K$ is a number field.

Analysis of two step nilsequences

Bernard Host, Bryna Kra (2008)

Annales de l’institut Fourier

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Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them. ...

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let $H \subset GL (V)$ be a connected complex reductive group where $V$ is a finite-dimensional complex vector space. Let $v \in V$ and let $G = {g \in GL (V) ∣ g H v = H v}$ . Following Raïs we say that the orbit $H v$ is if the identity component of $G$ is $H$ . If $H$ is semisimple, we say that $H v$ is for $H$ if the identity component of $G$ is an extension of $H$ by a torus. We classify the $H$ -orbits which are not (semi)-characteristic in many cases.

A Bochner type theorem for inductive limits of Gelfand pairs

Marouane Rabaoui (2008)

Annales de l’institut Fourier

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In this article, we prove a generalisation of Bochner-Godement theorem. Our result deals with Olshanski spherical pairs $(G, K)$ defined as inductive limits of increasing sequences of Gelfand pairs ${(G (n), K (n))}_{n \geq 1}$ . By using the integral representation theory of G. Choquet on convex cones, we establish a Bochner type representation of any element $ϕ$ of the set $𝒫^{♮} (G)$ of $K$ -biinvariant continuous functions of positive type on $G$ .

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field $F$ . We do this for automorphic representations of an arbitrary reductive group $G$ over $F$ , which is compact at infinity. In the special case where $G$ is an inner form of $GSp (4)$ over $ℚ$ , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.