Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → m → E → G(F) → 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN(K) → (under some assumption on the characteristic of k). Consider the category of G(O)-bi-invariant perverse sheaves on E with m-monodromy ζ. We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group ǦE,N. We compute the root datum of ǦE,N.
(Received September 25 2008)
(Accepted October 14 2008)
Key Wordsgeometric Langlands program; Satake isomorphism; monodromic perverse sheaves
AMS 2010 Mathematics subject classificationPrimary 14D24; Secondary 22E57; 11R39