• Corpus ID: 222208832

# On the determinant of representations of generalized symmetric groups.

@article{Amrutha2020OnTD,
title={On the determinant of representations of generalized symmetric groups.},
author={P. Amrutha and T. Geetha},
journal={arXiv: Representation Theory},
year={2020}
}
• Published 8 October 2020
• Mathematics
• arXiv: Representation Theory
In this paper we study the determinant of irreducible representations of the generalized symmetric groups $\mathbb{Z}_r \wr S_n$. We give an explicit formula to compute the determinant of an irreducible representation of $\mathbb{Z}_r \wr S_n$. Recently, several authors have characterized and counted the number of irreducible representations of a given finite group with nontrivial determinant. Motivated by these results, for given integer $n$, $r$ an odd prime and $\zeta$ a nontrivial…

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