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

2017/12/26 by Le, Tung, Magaard, Kay, Paolini, Alessandro
#20C15 #20C33 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1712.09263

Abstract

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 q^m/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 q^m/pⁱ where i > 1 which occurs in type D₆.

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