Green functions and higher Deligne--Lusztig characters

2018/07/09 by Chen, Zhe
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1807.02912

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 Gérardin'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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