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