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Perfect isometries between blocks of complex reflection groups. (English) Zbl 1455.20012

In the paper under review, the authors prove the following important result. Given any integers \(d\), \(e\), \(r\) and \(r'\), and a prime \(p\) not dividing \(d\cdot e\), any two blocks of the complex reflection groups \(G(de, e, r)\) and \(G(de, e, r')\) with the same \(p\)-weight are perfectly isometric.

MSC:

20C30 Representations of finite symmetric groups
20C15 Ordinary representations and characters
20C20 Modular representations and characters
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References:

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