Geodesic
Green Functions and Higher Deligne-Lusztig Characters
Documenta mathematica, Tome 23 (2018), pp. 2027-2041
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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.
DOI : 10.4171/dm/667
Classification : 14F20, 20C15, 20G99
Mots-clés : Deligne-Lusztig theory, reductive group schemes, Green functions, discrete valuation rings 
@article{10_4171_dm_667,
     author = {Zhe Chen},
     title = {Green {Functions} and {Higher} {Deligne-Lusztig} {Characters}},
     journal = {Documenta mathematica},
     pages = {2027--2041},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/667},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/667/}
}
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Zhe Chen. Green Functions and Higher Deligne-Lusztig Characters. Documenta mathematica, Tome 23 (2018), pp. 2027-2041. doi: 10.4171/dm/667

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