Irreducible tensor products over alternating groups
Let \(F\) be an algebraically closed field of characteristic \(p>5\), \(S_n\) and \(A_n\) the symmetric and alternating group on \(n\) letters, respectively. In the paper under review, the authors classify irreducible tensor products for modular representations of the group \(A_n\) over \(F\). The case \(p=0\) has been treated by the same authors [in Pac. J. Math. 190, No. 2, 201-223 (1999; Zbl 1009.20013)], but the cases \(p=2,3\) and \(5\) remain open. The corresponding results on the similar problem for the group \(S_n\) have been obtained by them [in Bull. Lond. Math. Soc. 32, No. 3, 292-296 (2000; Zbl 1021.20010)].
scientific article; zbMATH DE number 1471827