On pairs of matrices that satisfy certain polynomial identities

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Abstract

Let F be an arbitrary field, H be a subgroup of the symmetric group of degree m, Sm, λ be an irreducible F-valued character of H and dH λ be the generalizedmatrix function associated toH and λ. In this note we present some properties of the pairs (A, B) of m × m matrices over F that satisfy dH λ (AXB) = dH λ (X) for all X.We also describe the pairs (A, B) satisfying dH λ (AX) = dH λ (XB) for all X.
Original languageUnknown
Pages (from-to)1589-1605
JournalLinear Algebra and Its Applications
Volume436
Issue number6
DOIs
Publication statusPublished - 1 Jan 2012

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