Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale

Displaying similar documents to “Spherical conjugacy classes and the Bruhat decomposition”

Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace, Jean Lécureux (2011)

Annales de l’institut Fourier

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Let $X$ be a building of arbitrary type. A compactification $𝒞_{sph} (X)$ of the set ${Res}_{sph} (X)$ of spherical residues of $X$ is introduced. We prove that it coincides with the horofunction compactification of ${Res}_{sph} (X)$ endowed with a natural combinatorial distance which we call the . Points of $𝒞_{sph} (X)$ admit amenable stabilisers in $Aut (X)$ and conversely, any amenable subgroup virtually fixes a point in $𝒞_{sph} (X)$ . In addition, it is shown that, provided $Aut (X)$ is transitive enough, this compactification also coincides with the group-theoretic...

Proof of the Knop conjecture

Ivan V. Losev (2009)

Annales de l’institut Fourier

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In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.

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.

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.

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

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We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ of the group algebra of the Weyl group $W_{n}$ of type $B_{n}$ containing its usual Solomon algebra and the one of $𝔖_{n}$ : $Σ^{'} (W_{n})$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to $W_{n}$ . In an appendix, P. Baumann and C. Hohlweg present in an...