Flags and orbits of connected reductive groups over local rings

2019/04/01 by Chen, Zhe
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1904.00769

Abstract

We prove that generic higher Deligne-Lusztig representations over truncated formal power series are non-nilpotent, when the parameters are non-trivial on the biggest reduction kernel of the centre; we also establish a relation between the orbits of higher Deligne-Lusztig representations of SL_n and of GL_n. Then we introduce a combinatorial analogue of Deligne-Lusztig construction for general and special linear groups over local rings; this construction generalises the higher Deligne--Lusztig representations and affords all the nilpotent orbit representations, and for GL_n it also affords all the regular orbit representations as well as the invariant characters of the Lie algebra.

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