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arXiv · 1909.04460

Higher Lie characters and cyclic descent extension on conjugacy classes

Ron M. Adin·Pál Hegedüs·Yuval Roichman
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Abstract

A now-classical cyclic extension of the descent set of a permutation has been introduced by Klyachko and Cellini. Following a recent axiomatic approach to this notion, it is natural to ask which sets of permutations admit such an extension. The main result of this paper is a complete answer in the case of conjucay classes of permutations. It is shown that the conjugacy class of cycle type $\lambda$ has such an extension if and only if $\lambda$ is not of the form $(r^s)$ for some square-free $r$. The proof involves a detailed study of hook constituents in higher Lie characters.

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Ron M. Adin, Pál Hegedüs, Yuval Roichman. 2019-09-10. Higher Lie characters and cyclic descent extension on conjugacy classes. https://arxiv.org/abs/1909.04460

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