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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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Tilting exercises
We discuss tilting objects in categories of perverse sheaves smooth along some stratification. In case of the Schubert stratification we show that the Radon transform interchanges tilting,Expand
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Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution
We prove most of Lusztig’s conjectures on the canonical basis in homology of a Springer ber. The conjectures predict that this basis controls numerics of representations of the Lie algebra of aExpand
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Equivariant homology and K-theory of affine Grassmannians and Toda lattices
For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}[[{\rm t}]])$, we consider the equivariant homology $H^{G(\mathbb{C}[[{\rmExpand
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Intersection cohomology of Drinfeld‚s compactifications
Abstract. Let X be a smooth complete curve, G be a reductive group and $ P \subset G $ a parabolic. Following Drinfeld, one defines a (relative) compactification $ \widetilde{\hbox{\rm Bun}\,}_P $Expand
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Characteristic cycles for the loop Grassmannian and nilpotent orbits
α (X), which is a linear combination of closures of conormal bundles to submanifolds of X. Intuitively, the microlocal multiplicities cα() me asurethesingularity of at α. In settings related toExpand
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Semi-infinite flags. I. Case of global curve P 1 , Differential topology, infinite-dimensional Lie algebras, and applications
1.1. We learnt of the Semiinfinite Flag Space from B.Feigin and E.Frenkel in the late 80-s. Since then we tried to understand this remarkable object. It appears that it was essentially constructed,Expand
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