Decomposition numbers of Sp(4,q) for primes dividing \(q\pm 1\) (Q917685)

Let G be the finite symplectic group Sp(4,q) where q is odd. The author considers the r-blocks of G where r is an odd prime dividing \(q+1\) or q- 1. When the block is cyclic the Brauer trees (and hence the decomposition numbers) are known from a paper by \textit{P. Fong} and the reviewer [J. Algebra 131, 179-225 (1990; Zbl 0704.20011)]. Here the author considers those r-blocks which are not cyclic, hence of maximal defect. When r divides \(q+1\), he determines the decomposition numbers by elementary methods up to some ambiguities involving two unknown integer parameters. When r divides q-1 he uses results of \textit{L. Puig} [Astérisque 181- 182, 221-236 (1990)] to observe that the Brauer characters in blocks of maximal defect are liftable to ordinary characters, and then determines the decomposition numbers.