Research output: Contribution to journal › Article › peer-review

**Kronecker positivity and 2-modular representation theory**427 KB, PDF document

785 KB, PDF document

Journal | Transactions of the American Mathematical Society |
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Date | Accepted/In press - 2 Jul 2021 |

Date | E-pub ahead of print (current) - 10 Dec 2021 |

Volume | 8 |

Number of pages | 32 |

Pages (from-to) | 1024-1055 |

Early online date | 10/12/21 |

Original language | English |

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.

© 2021 by the authors

## Tensor and wreath products of symmetric groups

Project: Research project (funded) › Research

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