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Geometric Langlands duality and representations of algebraic groups over commutative rings
As such, it can be viewed as a first step in the geometric Langlands program. The connected complex reductive groups have a combinatorial classification by their root data. In the root datum theExpand
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Characteristic cycles of constructible sheaves
In his paper [K], Kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds: let X be a real analytic manifold, and F a complex of sheaves ofExpand
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Whittaker patterns in the geometry of moduli spaces of bundles on curves
Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack ofExpand
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Perverse Sheaves on affine Grassmannians and Langlands Duality
This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations ofExpand
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On the geometric Langlands conjecture
Let X be a (smooth, projective) curve and G be a reductive group over a finite field Fq. The field KX of rational functions on X is what number theorists call a global field and we can do the theoryExpand
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Characteristic cycles and wave front cycles of representations of reductive Lie groups
In the papers [V1] and [BV], Vogan and Barbasch-Vogan attach two similar invariants to representations of a reductive Lie group, one by an algebraic process, the other analytic. They conjectured thatExpand
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On the geometry of nilpotent orbits
In this paper we obtain various results about the geometry of nilpotent orbits. In particular, we obtain a better understanding of the Kostant-Sekiguchi correspondence and Kronheimer's instantonExpand
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A geometric Jacquet functor
In the paper [BB1], Beilinson and Bernstein used the method of localisation to give a new proof and generalisation of Casselman’s subrepresentation theorem. The key point is to interpret n-homologyExpand
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