The irreducible characters of the Sylow p-subgroups of the Chevalley groups D6(pf) and E6(pf). (November 2019) - Le, Tung; Magaard, Kay; Paolini, Alessandro
Abstract: We parametrize the set of irreducible characters of the Sylow p -subgroups of the Chevalley groups D 6 ( q ) and E 6 ( q ), for an arbitrary power q of any prime p . In particular, we establish that the parametrization is uniform for p ≥ 3 in type D 6 and for p ≥ 5 in type E 6, while the prime 2 in type D 6 and the primes 2, 3 in type E 6 yield character degrees of the form q m / p i which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters of a classical group of degree q m / p i where i > 1 which occurs in type D 6 .