Le symbole modéré
Lectures on spherical and wonderful varieties
These notes contain an introduction to the theory of spherical and wonderful varieties. We describe the Luna-Vust theory of embeddings of spherical homogeneous spaces, and explain how wonderful varieties fit in the theory.
Lemmes de zéros et nombres transcendants
Lifting differential operators from orbit spaces
Lifting mappings over invariants of finite groups.
Linear maps preserving orbits
Let be a connected complex reductive group where is a finite-dimensional complex vector space. Let and let . Following Raïs we say that the orbit is characteristic for if the identity component of is . If is semisimple, we say that is semi-characteristic for if the identity component of is an extension of by a torus. We classify the -orbits which are not (semi)-characteristic in many cases.
Linear models for reductive group actions on affine quadrics
Linear orbits of d-tuples of points in P1.
Linearization of group stack actions and the Picard group of the moduli of -bundles on a curve
Linearizing some actions on affine space
Localizations for construction of quantum coset spaces
Viewing comodule algebras as the noncommutative analogues of affine varieties with affine group actions, we propose rudiments of a localization approach to nonaffine Hopf algebraic quotients of noncommutative affine varieties corresponding to comodule algebras. After reviewing basic background on noncommutative localizations, we introduce localizations compatible with coactions. Coinvariants of these localized coactions give local information about quotients. We define Zariski locally trivial quantum...
Loop groups, elliptic singularities and principal bundles over elliptic curves
There is a well known relation between simple algebraic groups and simple singularities, cf. [5], [28]. The simple singularities appear as the generic singularity in codimension two of the unipotent variety of simple algebraic groups. Furthermore, the semi-universal deformation and the simultaneous resolution of the singularity can be constructed in terms of the algebraic group. The aim of these notes is to extend this kind of relation to loop groups and simple elliptic singularities. It is the...