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Abstract
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2separated 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 2height zero.
Original language  English 

Pages (fromto)  10241055 
Number of pages  32 
Journal  Transactions of the American Mathematical Society 
Volume  8 
Early online date  10 Dec 2021 
DOIs  
Publication status  Epub ahead of print  10 Dec 2021 
Bibliographical note
© 2021 by the authorsProjects
 1 Active

Tensor and wreath products of symmetric groups
4/05/21 → 3/05/26
Project: Research project (funded) › Research