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Twisted geometric Satake equivalence

Part of: Families, fibrations Lie groups

Published online by Cambridge University Press:  24 March 2010

Michael Finkelberg  and
Sergey Lysenko
Michael Finkelberg
Affiliation:
Independent Moscow University, Institute for Information Transmission Problems and State University Higher School of Economy, Department of Mathematics, 20 Myasnitskaya Street, Moscow 101000, Russia ([email protected])
Sergey Lysenko
Affiliation:
Institut Élie Cartan Nancy (Mathématiques), Université Henri Poincaré Nancy 1, BP 70239, 54506 Vandoeuvre-lés-Nancy Cedex, France ([email protected])
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Abstract

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.

Keywords

geometric Langlands programSatake isomorphismmonodromic perverse sheaves

MSC classification

Secondary: 14D24: Geometric Langlands program 22E57: Geometric Langlands program
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 4 , October 2010 , pp. 719 - 739
Copyright
Copyright © Cambridge University Press 2010

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