# 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}
}```
• Published 2 July 2015
• Mathematics
• Geometric and Functional Analysis
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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