Towards a Global Springer Theory II: the double affine action

Details Towards a Global Springer Theory II: the double affine action Towards a Global Springer Theory II: the double affine action

2009-04-22

arxiv.org/abs/0904.3371v1

Mathematics

Algebraic Geometry

47 pages

Scientific paper

We construct an action of the graded double affine Hecke algebra (DAHA) on the parabolic Hitchin complex, extending the affine Weyl group action constructed in \cite{GSI}. In particular, we get representations of the degenerate DAHA on the cohomology of parabolic Hitchin fibers. We also generalize our construction to {\em parahoric} versions of Hitchin stacks, including the construction of 'tHooft operators as a special case. We then study the interaction of the DAHA action and the cap product action given by the Picard stack acting on the parabolic Hitchin stack.

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