On the inductive blockwise Alperin weight condition for the unipotent blocks of finite groups of Lie type E_6

Abstract

In this article, we consider the finite exceptional groups of Lie type $E_6$ and ${}^2{E}_6$. We prove the inductive blockwise Alperin weight condition holds for unipotent $l$-blocks of $E_6^{\epsilon }(q)$ if $2,3\nmid q$, $l\ge 5$