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arXiv · 1807.02912

Green functions and higher Deligne--Lusztig characters

Zhe Chen
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Abstract

We give a generalisation of the character formula of Deligne--Lusztig representations from the finite field case to the truncated formal power series case. Motivated by this generalisation, we give a definition of Green functions for these local rings, and we prove some basic properties along the lines of the finite field case, like a summation formula. Among the applications we show that the higher Deligne--Lusztig characters and G\'erardin's characters agree at regular semisimple elements. We also derive a generalisation of Braverman and Kazhdan's result on gamma functions for Deligne--Lusztig characters, with a more elementary argument.

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Zhe Chen. 2018-07-09. Green functions and higher Deligne--Lusztig characters. https://arxiv.org/abs/1807.02912

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