# zbMATH — the first resource for mathematics

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 $$p=2$$.

##### MSC:
 20C33 Representations of finite groups of Lie type 20G05 Representation theory for linear algebraic groups 20G40 Linear algebraic groups over finite fields
##### Keywords:
decomposition numbers; finite Chevalley groups
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.