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Harish-Chandra theory is a significant tool in Lie theory, such as in the representation theory of Lie groups, Lie algebras and finite reductive groups. In this talk, we will discuss a generalisation of e-cuspidality in the generalised e-Harish-Chandra theory of finite reductive groups, and introduce the generic weights, which 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. Joint work with Gunter Malle and Jiping Zhang.