Chen, Zhe

Green Functions and Higher Deligne-Lusztig Characters

Doc. Math. 23, 2027-2041 (2018)
DOI: 10.25537/dm.2018v23.2027-2041
Communicated by Dan Ciubotaru


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 prove some basic properties along the lines of the finite field case, like a summation formula. As an application we show that the higher Deligne-Lusztig characters and Gérardin's characters agree at regular semisimple elements.

Mathematics Subject Classification

20G99, 14F20, 20C15


Deligne-Lusztig theory, reductive group schemes, Green functions, discrete valuation rings


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Chen, Zhe
Department of Mathematics, Shantou University, Guangdong, China