Adams operations and lambda-operations in beta-rings

Christopher D. Wensley; Ifor Morris

doi:10.1016/0012-365X(84)90053-0

Adams operations and lambda-operations in beta-rings

Christopher D. Wensley
, Ifor Morris

School of Computer Science & Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

In a lambda-ring there are operations lambda_{pi}, psi_{pi} and beta_{pi} for pi a partition of n. These operations are related by identities analogous to those between the symmetric functions a_{pi}, s_{pi} and h_{pi}. In a beta-ring there is defined an operation beta_H for [H] a conjugacy class of subgroups of the symmetric group S_n. This paper defines operations psi_H and lambda_H in a beta-rung such that whenever the beta-ring is a lambda-ring, and H a Young subgroup S_{pi} of S_n, then the beta_H, psi_H and lambda_H reduce to beta_{pi}, psi_{pi} and lambda_{pi} respectively. The identities relating the new operations are also investigated.

Original language	English
Pages (from-to)	253-270
Journal	Discrete Mathematics
Volume	50
DOIs	https://doi.org/10.1016/0012-365X(84)90053-0
Publication status	Published - 1984

Access to Document

10.1016/0012-365X(84)90053-0

Cite this

@article{6034daf15d114324b393eedeb33f8aa9,

title = "Adams operations and lambda-operations in beta-rings",

abstract = "In a lambda-ring there are operations lambda\_\{pi\}, psi\_\{pi\} and beta\_\{pi\} for pi a partition of n. These operations are related by identities analogous to those between the symmetric functions a\_\{pi\}, s\_\{pi\} and h\_\{pi\}. In a beta-ring there is defined an operation beta\_H for [H] a conjugacy class of subgroups of the symmetric group S\_n. This paper defines operations psi\_H and lambda\_H in a beta-rung such that whenever the beta-ring is a lambda-ring, and H a Young subgroup S\_\{pi\} of S\_n, then the beta\_H, psi\_H and lambda\_H reduce to beta\_\{pi\}, psi\_\{pi\} and lambda\_\{pi\} respectively. The identities relating the new operations are also investigated. ",

author = "Wensley, \{Christopher D.\} and Ifor Morris",

year = "1984",

doi = "10.1016/0012-365X(84)90053-0",

language = "English",

volume = "50",

pages = "253--270",

journal = "Discrete Mathematics",

issn = "1872-681X",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Adams operations and lambda-operations in beta-rings

AU - Wensley, Christopher D.

AU - Morris, Ifor

PY - 1984

Y1 - 1984

N2 - In a lambda-ring there are operations lambda_{pi}, psi_{pi} and beta_{pi} for pi a partition of n. These operations are related by identities analogous to those between the symmetric functions a_{pi}, s_{pi} and h_{pi}. In a beta-ring there is defined an operation beta_H for [H] a conjugacy class of subgroups of the symmetric group S_n. This paper defines operations psi_H and lambda_H in a beta-rung such that whenever the beta-ring is a lambda-ring, and H a Young subgroup S_{pi} of S_n, then the beta_H, psi_H and lambda_H reduce to beta_{pi}, psi_{pi} and lambda_{pi} respectively. The identities relating the new operations are also investigated.

AB - In a lambda-ring there are operations lambda_{pi}, psi_{pi} and beta_{pi} for pi a partition of n. These operations are related by identities analogous to those between the symmetric functions a_{pi}, s_{pi} and h_{pi}. In a beta-ring there is defined an operation beta_H for [H] a conjugacy class of subgroups of the symmetric group S_n. This paper defines operations psi_H and lambda_H in a beta-rung such that whenever the beta-ring is a lambda-ring, and H a Young subgroup S_{pi} of S_n, then the beta_H, psi_H and lambda_H reduce to beta_{pi}, psi_{pi} and lambda_{pi} respectively. The identities relating the new operations are also investigated.

U2 - 10.1016/0012-365X(84)90053-0

DO - 10.1016/0012-365X(84)90053-0

M3 - Article

SN - 1872-681X

VL - 50

SP - 253

EP - 270

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

Adams operations and lambda-operations in beta-rings

Abstract

Access to Document

Fingerprint

Cite this