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A note on decomposition numbers of \(G_2(2^n)\). (English) Zbl 1057.20009
Summary: The decomposition numbers of the finite Chevalley group \(G_2(p^n)\) of type \((G_2)\) defined over a finite field of characteristic \(r\) which divides \(p^n+1\) were almost determined by G. Hiss [J. Algebra 120, No. 2, 339-360 (1989; Zbl 0667.20009)]. The author proves that the decomposition numbers are bounded independently of \(p^n\) by using the same argument as T. Okuyama and K. Waki [J. Algebra 199, No. 2, 544-555 (1998; Zbl 0891.20009)] in the case of \(p=2\).

20C33 Representations of finite groups of Lie type
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
Full Text: DOI
[1] Carter, R.W., Finite groups of Lie type, Pure and appl. math., (1985) · Zbl 0458.20005
[2] Enomoto, H.; Yamada, H., The characters of G2(2n), Japan. J. math., 12, 2, (1986)
[3] Hiss, G., On the decomposition numbers of G2(q), J. algebra, 120, 339-360, (1989) · Zbl 0667.20009
[4] Okuyama, T.; Waki, K., Decomposition numbers of sp(4,q), J. algebra, 199, 544-555, (1998) · Zbl 0891.20009
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