Adjoint groups and the Mal'cev correspondence (a tale of four functors)
In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...
In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup .
The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them...
On étudie la relation entre le -rang des variétés abéliennes en caractéristique et la stratification de Kottwitz-Rapoport de la fibre spéciale en de l’espace de module des variétés abéliennes principalement polarisées avec structure de niveau de type Iwahori en . En particulier, on démontre la densité du lieu ordinaire dans cette fibre spéciale.