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Article

Twisted geometric Satake equivalence

Journal of the Institute of Mathematics Jussieu. 2010. Vol. 9. No. 4. P. 719-739.
Finkelberg M. V., Lysenko S.

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 → Gm → E → G(F) → 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character  : μN(k) → Q ℓ (under some assumption on the characteristic of k). Consider the category of G(O)- biinvariant perverse sheaves on E with Gm-monodromy . We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group ˇGE,N. We compute the root datum of ˇGE,N.