Twisted geometric Satake equivalence
Representation Theory
2023-08-25 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.0809.3738,
title = {Twisted geometric Satake equivalence},
author = {Michael Finkelberg and Sergey Lysenko},
journal= {arXiv preprint arXiv:0809.3738},
year = {2023}
}
Comments
22 pages, a reference to Lusztig is added. Final version to appear in J. of the Institute of Math. of Jussieu