ALGEBRAIC COMBINATORICS

no. 6
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, Volume 6 (2023) no. 6, pp. 1557-1591.

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.

Received:
Revised:
Accepted:
Published online:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Adin, Ron M.; Hegedüs, Pál; Roichman, Yuval. Higher Lie characters and cyclic descent extension on conjugacy classes. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1557-1591. doi : 10.5802/alco.323. https://alco.centre-mersenne.org/articles/10.5802/alco.323/

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