Dade's conjecture for 2-blocks of symmetric groups (Q1269425)

\textit{E. C. Dade} [Invent. Math. 109, No. 1, 187-210 (1992; Zbl 0738.20011)] conjectured that the number of ordinary irreducible characters of a finite group \(G\) in a \(p\)-block \(B\) with a fixed defect can be expressed as an alternating sum of the number of ordinary irreducible characters of related defects in related blocks \(B'\) of certain local \(p\)-subgroups of \(G\). This conjecture has been proved for the symmetric group where \(p\) is odd by \textit{J. B. Olsson} and \textit{K. Uno} [in J. Algebra 176, No. 2, 534-560 (1995; Zbl 0839.20018)]. In the paper under review, the author proves the conjecture for the symmetric group in the case of \(p=2\).