Kronecker positivity and 2-modular representation theory

Bessenrodt, C.; Bowman, C.; Sutton, L.

doi:10.1090/btran/70

Kronecker positivity and 2-modular representation theory
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by C. Bessenrodt, C. Bowman and L. Sutton HTML | PDF

Trans. Amer. Math. Soc. Ser. B 8 (2021), 1024-1055

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 $\mathfrak {S}_n$ which are of 2-height zero.

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