The irreducible characters of the Sylow p-subgroups of the Chevalley groups D₆(pᶠ) and E₆(pᶠ)

الأصل · EN

We parametrize the set of irreducible characters of the Sylow p-subgroups of the Chevalley groups D₆(q) and E₆(q), for an arbitrary power q of any prime p. In particular, we establish that the parametrization is uniform for p ≥ 3 in type D₆ and for p ≥ 5 in type E₆, while the prime 2 in type D₆ and the primes 2, 3 in type E₆ yield character degrees of the form qᵐ/pⁱ 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 qᵐ/pⁱ where i > 1 which occurs in type D₆.