Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre

Displaying similar documents to “Geometric Invariant Theory and Generalized Eigenvalue Problem II”

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.

Normality and non-normality of group compactifications in simple projective spaces

Paolo Bravi, Jacopo Gandini, Andrea Maffei, Alessandro Ruzzi (2011)

Annales de l’institut Fourier

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Given an irreducible representation $V$ of a complex simply connected semisimple algebraic group $G$ we consider the closure $X$ of the image of $G$ in $ℙ (End (V))$ . We determine for which $V$ the variety $X$ is normal and for which $V$ is smooth.

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.

Decomposition of reductive regular Prehomogeneous Vector Spaces

Hubert Rubenthaler (2011)

Annales de l’institut Fourier

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Let $(G, V)$ be a regular prehomogeneous vector space (abbreviated to $P V$ ), where $G$ is a reductive algebraic group over $ℂ$ . If $V = \oplus_{i = 1}^{n} V_{i}$ is a decomposition of $V$ into irreducible representations, then, in general, the PV’s $(G, V_{i})$ are no longer regular. In this paper we introduce the notion of quasi-irreducible $P V$ (abbreviated to $Q$ -irreducible), and show first that for completely $Q$ -reducible $P V$ ’s, the $Q$ -isotypic components are intrinsically defined, as in ordinary representation theory. We also show that, in an...

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.