Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace; Jean Lécureux

Displaying similar documents to “Combinatorial and group-theoretic compactifications of buildings”

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.

Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale (2009)

Annales de l’institut Fourier

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Let $G$ be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in $G$ as those intersecting only Bruhat cells in $G$ corresponding to involutions in the Weyl group of $G$ .

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 $G$ .

Billiard complexity in the hypercube

Nicolas Bedaride, Pascal Hubert (2007)

Annales de l’institut Fourier

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We consider the billiard map in the hypercube of $ℝ^{d}$ . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^{3 d - 3}$ is the order of magnitude of the complexity.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...