Isolated blocks in finite classical groups
The author classifies the isolated \(l\)-blocks of \(G=\text{Sp}(2n,q)\) or \(\text{SO}^\pm(2n,q)\) (\(q\) odd, \(l\) odd). The author proves an analogue of the classification theorem for unipotent blocks of \textit{M. Broué, G. Malle}, and \textit{J. Michel} [Astérisque 212, 7-92 (1993; Zbl 0843.20012)]. The author shows that an isolated block \(B\) associated with \((s)\) corresponds to a \(d\)-cuspidal pair \((L,\gamma)\) in the sense that the characters in \(B\) which correspond to \((s)\) under the Jordan decomposition are precisely the constitutents of \(R^G_L(\gamma)\). The author also proves a generalized or \(d\)-Harish-Chandra theory.
scientific article; zbMATH DE number 941273
scientific article