Vol. 62, No. 1, 1976

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Relations among generalized matrix functions

Russell L. Merris

Vol. 62 (1976), No. 1, 153–161
Abstract

Let G be a permutation group of degree m. Let λ be an irreducible, complex character of G. If A = (aij) is an m by m matrix, the generalized matrix function of A corresponding to G and λ is defined by

 G      ∑      ∏m
dλ(A ) =   λ(σ)   atσ(t).
σ∈G    t=1

We obtain relations among generalized matrix functions arising from G and those arising from a subgroup H of G. The methods yield some information about the corresponding symmetry classes of tensors.

Mathematical Subject Classification 2000
Primary: 15A45
Milestones
Received: 23 July 1975
Published: 1 January 1976
Authors
Russell L. Merris