On e-cuspidal pairs of finite groups of exceptional Lie type

Abstract

Let G be a simple, simply connected algebraic group of exceptional type defined over F q with Frobenius endomorphism F : G → G . Let ℓ ∤ q be a good prime for G . We determine the number of irreducible Brauer characters in the quasi-isolated ℓ -blocks of G F . This is done by proving that generalized e -Harish-Chandra theory holds for the Lusztig series associated to quasi-isolated elements of G ⁎ F .