We show that if Pm is a Sylow 2-subgroup of the finite symplectic group Sp2m(q), where q is a power of 2, then Pm has irreducible complex characters of degree 2-tqm(m-1)/2, where t is any integer satisfying 0≤t≤[m/2], and that qm(m-1)/2 is the largest possible degree of an irreducible complex character of Pm. We include related results on the degrees of the irreducible characters of a Sylow 2-subgroup of the split special orthogonal group SO+2m(q) when q is a power of 2. © 2001 Academic Press.
Gow, R., Marjoram, M., Previtali, A. (2001). On the irreducible characters of a Sylow 2-subgroup of the finite symplectic group in characteristic 2. JOURNAL OF ALGEBRA, 241(1), 393-409 [10.1006/jabr.2001.8755].
On the irreducible characters of a Sylow 2-subgroup of the finite symplectic group in characteristic 2
PREVITALI, ANDREA
2001
Abstract
We show that if Pm is a Sylow 2-subgroup of the finite symplectic group Sp2m(q), where q is a power of 2, then Pm has irreducible complex characters of degree 2-tqm(m-1)/2, where t is any integer satisfying 0≤t≤[m/2], and that qm(m-1)/2 is the largest possible degree of an irreducible complex character of Pm. We include related results on the degrees of the irreducible characters of a Sylow 2-subgroup of the split special orthogonal group SO+2m(q) when q is a power of 2. © 2001 Academic Press.
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