Parabolic Hecke eigensheaves

2019/10/06 by Donagi, Ron, Pantev, Tony · 2 citations
#14D20 #14D24 (Primary) #14H70 #32C38 (Secondary) #53D37 #58A14 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1910.02357

Abstract

We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line C with tame ramification at five points \p₁, p₂, p₃, p₄, p₅ \. In particular we construct the automorphic D-modules predicted by GLC on the moduli space of rank two parabolic bundles on (C, \p₁, p₂, p₃, p₄, p₅ \). The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers of the Hitchin fibration to reduce the problem to one in classical projective geometry on the intersection of two quadrics in ℙ⁴.

Cited by

• Cohomology of vector bundles on the moduli space of parabolic connections on ℙ¹ minus 5 points
• Monodromy Representations: Decomposing Rank-Three Bundles over the Projective Line with Three Marked Points

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