Higher Lie characters and cyclic descent extension on conjugacy classes

2019/09/10 by Adin, Ron M., Hegedüs, Pál, Roichman, Yuval · 1 citation
#05E05 #05E10 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1909.04460

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 λ has such an extension if and only if λ 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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• Asymptotics of higher Lie characters

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