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Nearby cycles of Whittaker sheaves on Drinfeld’s compactification

Part of: Lie groups

Published online by Cambridge University Press:  18 July 2018

Justin Campbell
Justin Campbell*
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA email campbell@math.harvard.edu
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Abstract

In this article we give a geometric construction of a tilting perverse sheaf on Drinfeld’s compactification, by applying the nearby cycles functor to a family of nondegenerate Whittaker sheaves. Its restrictions along the defect stratification are shown to be certain perverse sheaves attached to the nilpotent radical of the Langlands dual Lie algebra. We also describe the subquotients of the monodromy filtration using the Picard–Lefschetz oscillators introduced by Schieder. We give an argument that the subquotients are semisimple based on the action, constructed by Feigin, Finkelberg, Kuznetsov, and Mirković, of the Langlands dual Lie algebra on the global intersection cohomology of quasimaps into flag varieties.

Keywords

nearby cyclesDrinfeld’s compactificationtilting sheavesPicard–Lefschetz oscillatorsgeometric Langlands correspondence

MSC classification

Primary: 22E57: Geometric Langlands program
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 8 , August 2018 , pp. 1775 - 1800
Copyright
© The Author 2018 

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