Abstract
Let p be a prime number. In this article we study the restriction to \(\mathfrak {S}_{n-1}\) of irreducible characters of degree coprime to p of \(\mathfrak {S}_{n}\). In particular, we study the combinatorial properties of the subgraph \(\mathbb {Y}_{p^{\prime }}\) of the Young graph \(\mathbb {Y}\). This is an extension to odd primes of the work done in Ayyer et al. (2016) for p = 2.
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Acknowledgements
We thank Jason Long for suggesting Definition 5.10 and for many useful conversations on this topic. We are also grateful to the anonymous reviewer for several helpful comments.
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Presented by: Radha Kessar
The first author’s research was funded by Trinity Hall, University of Cambridge.
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Giannelli, E., Law, S. & Martin, S. On the p′-Subgraph of the Young Graph. Algebr Represent Theor 22, 627–650 (2019). https://doi.org/10.1007/s10468-018-9791-7
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DOI: https://doi.org/10.1007/s10468-018-9791-7