Unramified representations of reductive groups over finite rings

TL;DR

This paper extends Lusztig's construction of representations from finite fields to more general finite local rings using advanced algebraic tools, broadening the scope of representation theory for reductive groups.

Contribution

It generalizes Lusztig's results to reductive groups over arbitrary finite local rings employing the Greenberg functor and group scheme theory.

Findings

Extended Lusztig's construction to finite local rings

Utilized Greenberg functor and group schemes

Broadened understanding of representations over finite rings

Abstract

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig's results to reductive groups over arbitrary finite local rings. This generalization uses the Greenberg functor and the theory of group schemes over Artinian local rings.