Vol. 50, No. 2, 1974

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An identity for matrix functions

Russell L. Merris

Vol. 50 (1974), No. 2, 557–562
Abstract

Let G Sn. Let η be a character on G. For A = (aij) an n-square matrix, define

 G      ∑      ∏n
dη (A ) =   η(g)   atg(t).
g∈G    t=1

A general identity for idempotents in group algebras is proved. A very special example of the consequences is this: If χ is a linear character on G and H a normal subgroup of G, then [G : H]dχH(A) = η(1)dηG(A), where the summation is over those irreducible characters η of G whose restriction to H contain χ as a component.

Mathematical Subject Classification 2000
Primary: 15A15
Milestones
Received: 4 October 1972
Published: 1 February 1974
Authors
Russell L. Merris