Geodesic
Higher Lie characters and cyclic descent extension on conjugacy classes
Adin, Ron M.1 ; Hegedüs, Pál2 ; Roichman, Yuval1
1 Department of Mathematics Bar-Ilan University Ramat-Gan 52900 Israel
2 Department of Algebra Institute of Mathematics Budapest University of Technology and Economics Műegyetem rkp. 3 H-1111 Budapest Hungary
Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1557-1591

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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 a (not necessarily classical) extension.

The main result of this paper is a complete answer in the case of conjugacy 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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DOI : 10.5802/alco.323
Classification : 05E10, 05E05, 20B30, 20C30
Keywords: Cyclic descent, conjugacy class, symmetric group, higher Lie character, hook constituent

Adin, Ron M. 1 ; Hegedüs, Pál 2 ; Roichman, Yuval 1

1 Department of Mathematics Bar-Ilan University Ramat-Gan 52900 Israel
2 Department of Algebra Institute of Mathematics Budapest University of Technology and Economics Műegyetem rkp. 3 H-1111 Budapest Hungary
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Higher {Lie} characters and cyclic descent extension on conjugacy classes},
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     pages = {1557--1591},
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Adin, Ron M.; Hegedüs, Pál; Roichman, Yuval. Higher Lie characters and cyclic descent extension on conjugacy classes. Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1557-1591. doi: 10.5802/alco.323

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