On Auslander-Reiten components and simple modules for finite groups of Lie type (Q5937404)

Let \(k\) be an algebraically closed field of characteristic \(p\) and let \(kG\) be the group algebra of the finite group \(G\) over \(k\). Let \(B\) be a \(p\)-block of \(kG\) with \(D\) as a defect group. Then \(B\) is said to be of wild representation type if \(D\) is neither cyclic, dihedral, semi-dihedral nor generalized quaternion.NEWLINENEWLINENEWLINEThe main result of this paper is: Theorem: Let \(G\) be a finite group of Lie type defined over a finite field \(K\) of characteristic \(p\). Let \(B\) be a block of \(kG\) with full defect and of wild representation type. Then any simple \(kG\)-module \(S\) of \(B\) lies at the end of its Auslander-Reiter component \(\Theta(S)\).