A formula for the geometric Jacquet functor and its character sheaf analogue

@article{Chen2015AFF,
  title={A formula for the geometric Jacquet functor and its character sheaf analogue},
  author={Tsao-Hsien Chen and Alexander Yom Din},
  journal={Geometric and Functional Analysis},
  year={2015},
  volume={27},
  pages={772-797}
}
Let (G,K) be a symmetric pair over the complex numbers, and let $${X=K \backslash G}$$X=K\G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a degeneration of X to $${MN \backslash G}$$MN\G, which we call the “wonderful degeneration”. We show that on the category of character sheaves on X, this functor is isomorphic to a composition of two averaging functors (a parallel result, on the level of functions in the p-adic setting, was obtained in [BK… 

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