On semisimple classes and semisimple characters in finite reductive groups

Olivier Brunat

Displaying similar documents to “On semisimple classes and semisimple characters in finite reductive groups”

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...

Kac-Moody groups, hovels and Littelmann paths

Stéphane Gaussent, Guy Rousseau (2008)

Annales de l’institut Fourier

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We give the definition of a kind of building $ℐ$ for a symmetrizable Kac-Moody group over a field $K$ endowed with a discrete valuation and with a residue field containing $ℂ$ . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if $K = ℂ ((t))$ , the geodesic...

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.

Lattices and harmonic analysis on some 2-step solvable Lie groups.

Huang, Huale (2003)

Journal of Lie Theory

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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.