Perverse Sheaves on a Loop Group and Langlands’ Duality
نویسنده
چکیده
on the set of F-rational points of X given by the alternating sum of traces of Fr, the Frobenius action on stalks of the cohomology sheaves HiF . He then went on to initiate an ambitious program of giving geometric (= sheaf theoretic) meaning to various classical algebraic formulas via the above “functions-faisceaux” correspondence F 7→ χ F . This program got a new impetus with the discovery of perverse sheaves [BBD], for it happens for certain mysterious reasons that most of the functions encountered ‘in nature’ arise via the “functions-faisceaux” correspondence from perverse sheaves. In the present paper Grothendieck’s philosophy is applied to what may be called the Geometric Langlands duality. The relevance of the intersection cohomology technique to our problem was first pointed out by Drinfeld [D] and Lusztig [Lu 1]. Later, in the remarkable paper [Lu], Lusztig established algebraically a surprising connection between finite-dimensional representations of a semisimple Lie algebra and the Kazhdan-Lusztig polynomials for an affine Weyl group. It is one
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