Integrable Crystals and Restriction to Levi Subgroups Via Generalized Slices in the Affine Grassmannian |
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Authors: | Email author" target="_blank">V?V?KrylovEmail author |
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Institution: | 1.Department of Mathematics,National Research University Higher School of Economics,Moscow,Russia |
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Abstract: | Let G be a connected reductive algebraic group over ?, and let Λ G + be the monoid of dominant weights of G. We construct integrable crystals BG(λ), λ ∈ Λ G + , using the geometry of generalized transversal slices in the affine Grassmannian of the Langlands dual group of G. We also construct tensor product maps \(P{\lambda _1},{\lambda _2}:{B^G}({\lambda _2}) \to {B^G}({\lambda _1} + {\lambda _2}) \cup \{ 0\} \) in terms of multiplication in generalized transversal slices. Let L ? G be a Levi subgroup of G. We describe the functor Res L G : Rep(G) → Rep(L) of restriction to L in terms of the hyperbolic localization functors for generalized transversal slices. |
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