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Commutators and Itô’s theorem on character degrees. (Kommutatoren und Itô’s Satz über Charaktergrade.) (German) Zbl 0890.20009

The aim of this paper is to provide, what is called, easy accessible proofs of Theorems of N. Itô [Nagoya Math. J. 3, 5-6 (1951; Zbl 0043.26002)], of C. W. Curtis and T. V. Fossum [Math. Z. 107, 402-406 (1968; Zbl 0185.06801)]and of G. Keller [ibid. 107, 221-224 (1968; Zbl 0186.32801)]. Methods used here are: orthogonality relations, the center of \(\mathbb{C}[{\mathcal G}]\), some linear algebra, reciprocity law of Frobenius, Hecke-algebra-structure-constants; almost no algebraic number theory is used.

MSC:

20C15 Ordinary representations and characters
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References:

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