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Kronecker positivity and 2-modular representation theory

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JournalTransactions of the American Mathematical Society
DateAccepted/In press - 2 Jul 2021
DateE-pub ahead of print (current) - 10 Dec 2021
Volume8
Number of pages32
Pages (from-to)1024-1055
Early online date10/12/21
Original languageEnglish

Abstract

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.

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© 2021 by the authors

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