Bessenrodt, Christine; Kleshchev, Alexander S. On tensor products of modular representations of symmetric groups. (English) Zbl 1021.20010 Bull. Lond. Math. Soc. 32, No. 3, 292-296 (2000). Main Theorem: Let \(D^\lambda\) and \(D^\mu\) be two irreducible \(F\Sigma_n\)-modules of dimensions greater than 1. Assume that \(D^\lambda\otimes D^\mu\) is irreducible. Then \(p=2\), \(n\) is even, and if \[ \lambda=(\lambda_1>\lambda_2>\cdots>\lambda_r>0)\quad\text{and}\quad\mu=(\mu_1>\mu_2>\cdots>\mu_s>0), \] then \(\lambda_1\equiv\lambda_2\equiv\cdots\equiv\lambda_r\pmod 2\) or \(\mu_1\equiv\mu_2\equiv\cdots\equiv\mu_s\pmod 2\) (or both). Cited in 1 ReviewCited in 14 Documents MSC: 20C30 Representations of finite symmetric groups 20C20 Modular representations and characters Keywords:tensor products; modular representations; symmetric groups; irreducible modules PDFBibTeX XMLCite \textit{C. Bessenrodt} and \textit{A. S. Kleshchev}, Bull. Lond. Math. Soc. 32, No. 3, 292--296 (2000; Zbl 1021.20010) Full Text: DOI