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Twisted geometric Satake equivalence
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 9 / Issue 4 / October 2010
- Published online by Cambridge University Press:
- 24 March 2010, pp. 719-739
- Print publication:
- October 2010
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- Article
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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.
(under some assumption on the characteristic of k). Consider the category of 