Twisted geometric Satake equivalence

Details Twisted geometric Satake equivalence Twisted geometric Satake equivalence

2008-09-22

arxiv.org/abs/0809.3738v3

Mathematics

Representation Theory

22 pages, a reference to Lusztig is added. Final version to appear in J. of the Institute of Math. of Jussieu

Scientific paper

We generalize the classical Satake equivalence as follows. Let k be an algebraically closed field, set O=k[[t]] and F=k((t)). For an almost simple algebraic group G we classify central extensions of G(F) by the multiplicative group. Any such extension E splits canonically over G(O). Consider the category of G(O)-biinvariant perverse sheaves on E with a given Gm-monodromy . We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group. We compute the root datum of this group.

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