Mirković, Ivan; Vilonen, Kari Perverse sheaves on affine Grassmannians and Langlands duality. (English) Zbl 0987.14015 Math. Res. Lett. 7, No. 1, 13-24 (2000). 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. Reviewer: Alexei Rudakov (Trondheim) Cited in 7 ReviewsCited in 39 Documents MSC: 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) Keywords:Satake isomorphism; Langlands duality; perverse sheaves; affine Grassmannian PDF BibTeX XML Cite \textit{I. Mirković} and \textit{K. Vilonen}, Math. Res. Lett. 7, No. 1, 13--24 (2000; Zbl 0987.14015) Full Text: DOI