The Brauer trees of the exceptional Chevalley groups of type \(F_4\) and \(^2E_6\) (Q1383558)

The authors determine the Brauer trees of the cyclic unipotent blocks of finite Chevalley groups of type \(F_4(q)\) and of type \({^2E_6}(q)\). In the latter case one tree remains open in case \(q\not\equiv-1\bmod 3\). This work is part of a program to determine all Brauer trees for all finite groups. For finite groups of Lie type, only Brauer trees for groups of type \(E_7\) and \(E_8\), together with the above-mentioned exception in case \({^2E_6}(q)\), remain open.