Wonderful varieties of type $\mathsf E$
نویسندگان
چکیده
منابع مشابه
Wonderful Varieties of Type E
The classification of spherical varieties is already known for semisimple groups of types A and D. Adding type E, we complete the classification for all semisimple groups with a simply laced Dynkin diagram.
متن کاملWonderful Varieties of Type D
Let G be a connected semisimple group over C, whose simple components have type A or D. We prove that wonderful G-varieties are classified by means of combinatorial objects called spherical systems. This is a generalization of a known result of Luna for groups of type A; thanks to another result of Luna, this implies also the classification of all spherical G-varieties for the groups G we are c...
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We show that the proof of Luna’s conjecture about the classification of general wonderful G-varieties can be reduced to the analysis of finitely many families of primitive cases. We work out all primitive cases arising with any classical group G. Luna’s conjecture states that, for any semisimple complex algebraic group G, wonderful G-varieties are classified by spherical systems of G ([12]). Th...
متن کاملAutomorphisms of Wonderful Varieties
Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut(X) and we calculate Luna’s invariants of X under its action.
متن کاملSimple Immersions of Wonderful Varieties
Let G be a semisimple connected linear algebraic group over C, and X a wonderful G-variety. We study the possibility of realizing X as a closed subvariety of the projective space of a simple G-module. For any wonderful variety X we give a necessary and sufficient condition in terms of its set of spherical roots, which are certain characters of B (a fixed Borel subgroup of G) associated to the G...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2007
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-07-00318-4