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We give an interpretation of the path model of a representation [ 18 ] of a complex semisimple algebraic group G in terms of the geometry of its affine Grassmannian. In this setting, the paths are replaced by LS—galleries in the affine Coxeter complex associated to the Weyl group of G. We determine those galleries such that the associated cell has a non-empty intersection with G C [ [ t ] ]. The aim of the present article is to provide a connection between the path model [ 18 ] for finite dimensional representations of a connected complex semisimple algebraic group G and the geometry of the affine Grassmann variety G. As a byproduct of this interpretation, we associate in a canonical way to each path or rather gallery in a path model of a representation one of the algebraic cycles occurring in the work of Mirkovic and Vilonen [ 24 ]. Another object which comes into the picture is the affine Tits—building J a associated to G.

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LS gallery Art

[math/v2] LS-Galleries, the path model and MV-cycles

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Gaussent and P. Gaussent , P. Littelmann Published Mathematics Duke Mathematical Journal We give an interpretation of the path model of a representation [18] of a complex semisimple algebraic group G in terms of the geometry of its affine Grassmannian. In this setting, the paths are replaced by LS—galleries in the affine Coxeter complex associated to the Weyl group of G.

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LS galleries, the path model, and MV cycles

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