Twisted Geometric Satake Equivalence
نویسندگان
چکیده
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 ζ : 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 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 .
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