Irreducible tensor products of representations of symmetric and related groups

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In general, given 2 irreducible representations of dimension greaterthan 1 of a given group, their tensor product is not irreducible. Thereare though some cases were this happens. Starting from recentresults of the applicant about such irreducible tensor products forsymmetric and alternating groups, the aim of this project is to classifyirreducible tensor products of 2 representations of dimension greaterthan 1 for alternating groups and covering groups of symmetric andalternating groups.