Towards a Global Springer Theory III: Endoscopy and Langlands duality

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dc.creatorYun, Zhiwei
dc.date2009-04-22
dc.date.accessioned2026-07-07T13:07:12Z
dc.date.available2026-07-07T13:07:12Z
dc.descriptionWe prove three new results about the global Springer action defined in \cite{GSI}. The first one determines the support of the perverse cohomology sheaves of the parabolic Hitchin complex, which serves as a technical tool for the next results. The second one (the Endoscopic Decomposition Theorem) links certain direct summands of the parabolic Hitchin complex of $G$ to the endoscopic groups of $G$. This result generalizes Ngô's geometric stabilization of the trace formula in \cite{NgoFL}. The third result links the stable parts of the parabolic Hitchin complexes for Langlands dual groups, and establishes a relation between the global Springer action on one hand and certain Chern class action on the other. This result is inspired by the mirror symmetry between dual Hitchin fibrations. Finally, we present the first nontrivial example in the global Springer theory.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/0904.3372
dc.identifierhttp://arxiv.org/abs/0904.3372
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228013
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14H60; 20G35; 14F20; 14K30
dc.titleTowards a Global Springer Theory III: Endoscopy and Langlands duality
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