Kronecker positivity and 2-modular representation theory

Chris Bowman-Scargill, Christine Bessenrodt, Louise Sutton

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This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these results and other modular representation theoretic techniques on the study of Kronecker coefficients and hence verify Saxl’s conjecture for several large new families of partitions. In particular, we verify Saxl’s conjecture for all irreducible characters of the symmetric group which are of 2-height zero.
Original languageEnglish
Pages (from-to)1024-1055
Number of pages32
JournalTransactions of the American Mathematical Society
Early online date10 Dec 2021
Publication statusE-pub ahead of print - 10 Dec 2021

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