Casimir-Operator und ein Satz von Reynolds über Charaktergrade
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The following result concerning character degrees is familiar. Let H be a normal subgroup of the finite group G with the identity e. Furthermore let \(\theta \) be an irreducible complex character of H, and \(\chi \) be an irreducible complex character of G with \(\big (\theta ^G,\chi \big )_G \ne 0\). Then the co-degree \(|H|/\theta (e)\) divides the co-degree \(|G|/\chi (e)\). The usual proof rests on Schur's theory of projective representations and on Clifford's theory. The purpose of this paper is to give a more elementary proof based on the so-called Casimir operator.
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