Affine Deligne–Lusztig varieties in affine flag varieties
نویسندگان
چکیده
منابع مشابه
Affine Deligne-lusztig Varieties in Affine Flag Varieties
This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.
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Affine Deligne-Lusztig varieties are analogs of DeligneLusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine DeligneLusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a...
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The Littelmann path model gives a realisation of the crystals of integrable representations of symmetrizable Kac-Moody Lie algebras. Recent work of Gaussent-Littelmann [GL] and others [BG] [GR] has demonstrated a connection between this model and the geometry of the loop Grassmanian. The alcove walk model is a version of the path model which is intimately connected to the combinatorics of the a...
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The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal torus of G are smooth irreducible locally closed subvarieties of G/P , isomorphic to intersections of dual Schubert cells in the full flag variety G/B of G, and their Zariski closures are explicitly com...
متن کاملPoisson Structures on Affine Spaces and Flag Varieties
The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal torus of G are smooth irreducible locally closed subvarieties of G/P , isomorphic to intersections of dual Schubert cells in the full flag variety G/B of G, and their Zariski closures are explicitly com...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2010
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x10004823