Stability of decomposition numbers for finite Chevalley groups (Q1265532)

Let \(G\) be a finite Chevalley group defined over a field \(F_q\), where \(q=p^n\), \(p\) a prime. The ordinary irreducible characters of \(G\) are denoted by \(R_w(n,\mu)\) and are obtained by decomposing the Deligne-Lusztig characters. Here \(w\) is in the Weyl group and \(\mu\) is in the weight lattice. Let \(\psi(n,\lambda)\) denote a certain projective indecomposable character of \(G\) and consider it as a Brauer character. In this case \(\psi(n,\lambda)\) can be decomposed into characters \(R_w(n,\mu)\). In this paper the author shows that for large enough \(p\) and fixed \(\lambda\) and \(\mu\) the decomposition number given by the multiplicity of \(R_w(n,\mu)\) in \(\psi(n,\lambda)\) becomes stable as \(n\) becomes large.