Generic weights for finite reductive groups

This paper is motivated by the study of Alperin’s weight conjecture in the representation theory of finite groups. We generalize the notion of e -cuspidality in the e -Harish-Chandra theory of finite reductive groups, and define generic weights in non-defining characteristic. We show that the generic weights play an analogous role as the weights defined by Alperin in the investigation of the inductive Alperin weight condition for simple groups of Lie type at most good primes. We hope that our approach will constitute a major step towards a proof of Alperin’s weight conjecture.