Kronecker positivity and 2-modular representation theory

TY - JOUR

T1 - Kronecker positivity and 2-modular representation theory

AU - Bowman-Scargill, Chris

AU - Bessenrodt, Christine

AU - Sutton, Louise

N1 - © 2021 by the authors

PY - 2021/12/10

Y1 - 2021/12/10

N2 - 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.

AB - 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.

U2 - 10.1090/btran/70

DO - 10.1090/btran/70

M3 - Article

SN - 0002-9947

VL - 8

SP - 1024

EP - 1055

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -