### Abstract

In this paper, we give the decomposition into irreducible characters of the restriction to the wreath product Zp−1 o Sw of any irreducible character of (Zp o Zp−1) o Sw, where p is any odd prime, w ≥ 0 is an integer, and Zp and Zp−1 denote the cyclic groups of order p and p − 1 respectively. This answers the question of how to decompose the restrictions to p-regular elements of irreducible characters of the symmetric group Sn in the Z-basis corresponding to the p-basic set of Sn described by Brunat and Gramain in [1]. The result is given in terms of the Littlewood-Richardson coefficients for the symmetric group.

Original language | English |
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Pages (from-to) | 2428-2441 |

Number of pages | 14 |

Journal | Communications in Algebra |

Volume | 48 |

Issue number | 6 |

Early online date | 30 Jan 2020 |

DOIs | |

Publication status | Published - 2020 |

### Keywords

- basic sets
- character theory
- representation theory
- symmetric group
- wreath products
- Basic sets

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Gramain, J-B., & Marciuk, A. (2020). Restriction of characters to subgroups of wreath products and basic sets for the symmetric group.

*Communications in Algebra*,*48*(6), 2428-2441. https://doi.org/10.1080/00927872.2020.1714638