Local structure of the p-blocks of \(\tilde S_ n\)
Local block theory was introduced by \textit{J. Alperin} and \textit{M. Broué} [Ann. Math., II. Ser. 110, 143-157 (1979; Zbl 0416.20006)] generalizing both ideas of R. Brauer and local analysis in finite group theory. The main concept in local block theory is the notion of subpairs of a block and inclusions between them. These objects were determined in the case of the symmetric groups by \textit{L. Puig} [Publ. Math. Univ. Paris VII 25, 171-189 (1987; Zbl 0639.20009)] and in the case of the general linear and unitary groups by \textit{M. Broué} [Astérisque 133/134, 159-187 (1986)]. In the present paper the author describes the subpairs and their inclusions (in odd characteristic) for the 2-fold covering groups of the symmetric groups. It turns out that the combinatorial algorithm of the removal of a p-bar has an algebraic interpretation as the inclusion of subpairs; this is similar to the case of the symmetric groups. A consequence of the results in this paper is a new proof of the Morris conjecture. This had been established earlier by \textit{J. F. Humphreys} [in J. Lond. Math. Soc., II. Ser. 33, 441-452 (1986; Zbl 0633.20007)] in a different way.
scientific article; zbMATH DE number 4053887