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

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

Annales de l’institut Fourier

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 inverse images...

Admissibility for quasiregular representations of exponential solvable Lie groups

Vignon Oussa (2013)

Colloquium Mathematicae

Let N be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra of dimension n. Let H be a subgroup of the automorphism group of N. Assume that H is a commutative, simply connected, connected Lie group with Lie algebra . Furthermore, assume that the linear adjoint action of on is diagonalizable with non-purely imaginary eigenvalues. Let τ = I n d H N ⋊ H 1 . We obtain an explicit direct integral decomposition for τ, including a description of the spectrum as a submanifold of (+)*, and a...

A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups

D. Müller, E. Prestini (2010)

Colloquium Mathematicae

We define partial spectral integrals S R on the Heisenberg group by means of localizations to isotropic or anisotropic dilates of suitable star-shaped subsets V containing the joint spectrum of the partial sub-Laplacians and the central derivative. Under the assumption that an L²-function f lies in the logarithmic Sobolev space given by l o g ( 2 + L α ) f ∈ L ² , where L α is a suitable “generalized” sub-Laplacian associated to the dilation structure, we show that S R f ( x ) converges a.e. to f(x) as R → ∞.

A.e. convergence of spectral sums on Lie groups

Christopher Meaney, Detlef Müller, Elena Prestini (2007)

Annales de l’institut Fourier

Let ℒ be a right-invariant sub-Laplacian on a connected Lie group G , and let S R f : = ∫ 0 R d E λ f , R ≥ 0 , denote the associated “spherical partial sums,” where ℒ = ∫ 0 ∞ λ d E λ is the spectral resolution of ℒ . We prove that S R f ( x ) converges a.e. to f ( x ) as R → ∞ under the assumption log ( 2 + ℒ ) f ∈ L 2 ( G ) .

Algebraic aspects of web geometry

Maks A. Akivis, Vladislav V. Goldberg (2000)

Commentationes Mathematicae Universitatis Carolinae

Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.

Algebraic loop groups and moduli spaces of bundles

Gerd Faltings (2003)

Journal of the European Mathematical Society

We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.

Currently displaying 261 – 280 of 434