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Perverse sheaves on affine Grassmannians and Langlands duality. (English) Zbl 0987.14015
The paper outlines the construction of the Langlands duality, i.e. the equivalent of the category of \(k\)-representations of the Langlands dual group \(^LG\) and the category of perverse sheaves with coefficients in \(\mathbb{K}\) on the affine Grassmannian associated in \(G\) for a complex algebraic reductive group \(G\). The result for \(\mathbb{K}\) the field of complex numbers is due to V. Ginzburg (alg-geom/9511007). The authors generalize it to any commutative ring \(\mathbb{K}\), and claim new proofs for some crucial steps of the complex case, but the text only outlines the constructions and announces the results.

14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14M15 Grassmannians, Schubert varieties, flag manifolds
20G05 Representation theory for linear algebraic groups
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
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