Noncommutative cyclic characters of symmetric groups
type: Item
instance of: scholarly article
title: Noncommutative cyclic characters of symmetric groups
zbMATH Open document ID: 0857.20005
author: Bernard Leclerc
author: Thomas Scharf
author: Jean-Yves Thibon
published in: Journal of Combinatorial Theory. Series A
publication date: 1997-03-03T00:00:00Z
review text: This paper is based on the recent development of a theory of noncommutative symmetric functions (instead of being polynomials, these involve noncommuting indeterminates). There is a well-known connection between symmetric functions (also Schur-functions, descent algebras, etc.) and characters of symmetric groups. In particular, the characters induced by transitive cyclic subgroups (of a symmetric group) correspond to certain symmetric functions with a rich combinatorial structure, and this paper discusses analogues of those in the context of noncommutative symmetric functions. The main result is a multiplication formula for these noncommutative cyclic characters. The commutative projection of this formula gives a combinatorial formula for the Kronecker product of two cyclic representations of the symmetric group. The authors also give an interpretation of this formula as a multiplicative property of the major index of permutations.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 909613
zbMATH Keywords: noncommutative symmetric functions
zbMATH Keywords: noncommuting indeterminates
zbMATH Keywords: Schur functions
zbMATH Keywords: descent algebras
zbMATH Keywords: characters of symmetric groups
zbMATH Keywords: transitive cyclic subgroups
zbMATH Keywords: multiplication formula
zbMATH Keywords: noncommutative cyclic characters
zbMATH Keywords: Kronecker product
zbMATH Keywords: cyclic representations
zbMATH Keywords: major index of permutations
reviewed by: Albert J. Goodman
MaRDI profile type: Publication
OpenAlex ID: W2026990364
DOI: 10.1006/JCTA.1996.0063
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description: scientific article; zbMATH DE number 909613