Generically Transitive Actions on Multiple Flag Varieties
نویسندگان
چکیده
منابع مشابه
Generically Multiple Transitive Algebraic Group Actions
With every nontrivial connected algebraic group G we associate a positive integer gtd(G) called the generic transitivity degree of G and equal to the maximal n such that there is a nontrivial action of G on an irreducible algebraic variety X for which the diagonal action of G on Xn admits an open orbit. We show that gtd(G) 6 2 (respectively, gtd(G) = 1) for all solvable (respectively, nilpotent...
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Let G be a split semisimple algebraic group over an arbitrary field F , let E be a G-torsor over F , and let P be a parabolic subgroup of G. The quotient variety X := E/P , known as a flag variety, is generically split, if the parabolic subgroup P is special. It is generic, provided that the G-torsor E over F is a standard generic Gk-torsor for a subfield k ⊂ F and a split semisimple algebraic ...
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We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety E/P is torsion-free, where P ⊂ G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of E/P include the Severi-B...
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We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives.
متن کاملSymplectic Multiple Flag Varieties of Finite Type
Problem: Given a reductive algebraic group G, find all k-tuples of parabolic subgroups (P1, . . . , Pk) such that the product of flag varieties G/P1 × · · · ×G/Pk has finitely many orbits under the diagonal action of G. In this case we call G/P1× · · · ×G/Pk a multiple flag variety of finite type. In this paper, we solve this problem for the symplectic group G = Sp2n. We also give a complete en...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2013
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnt019