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

VL - 50

SP - 253

EP - 270

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 1872-681X

ER -