Penrose transform and monogenic sections

Tomáš Salač

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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.

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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...

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Linear maps preserving orbits

Gerald W. Schwarz (2012)

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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.