Displaying similar documents to “Equations of some wonderful compactifications”

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let H ⊂ GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v ∈ V and let G = { g ∈ 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.

Adjoint representation of E 8 and del Pezzo surfaces of degree 1

Vera V. Serganova, Alexei N. Skorobogatov (2011)

Annales de l’institut Fourier

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Let X be a del Pezzo surface of degree 1 , and let G be the simple Lie group of type E 8 . We construct a locally closed embedding of a universal torsor over X into the G -orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Néron-Severi torus T of X identified with a maximal torus of G extended by the group of scalars. Moreover, the T -invariant hyperplane sections of the torsor defined by the roots of G are the...

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 = ⊕ 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...

Surprising properties of centralisers in classical Lie algebras

Oksana Yakimova (2009)

Annales de l’institut Fourier

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Let 𝔤 be a classical Lie algebra, , either 𝔤𝔩 n , 𝔰𝔭 n , or 𝔰𝔬 n and let e be a nilpotent element of 𝔤 . We study various properties of the centralisers 𝔤 e . The first four sections deal with rather elementary questions, like the centre of 𝔤 e , commuting varieties associated with 𝔤 e , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on 𝔤 e * and symmetric invariants of 𝔤 e .

Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite p -group G acting on a smooth projective curve X over an algebraically closed field k of characteristic p , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of G acting on the space V of global holomorphic quadratic differentials on X . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when G is cyclic or when the action of G on...