In representation theory of finite groups, there is a well known Mackey irreducibility test for irreducibility of an induced representation to be irreducible (Serre- Linear Representations of Finite Groups - #7.4). The author has stated it for field $\mathbb{C}$. Is it true for representations over arbitrary field whose characteristic is zero or co-prime to the order of group ?
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Mackey Irreducibility Criteriaof Induced Representation over arbitrary fieldIn representation theory of finite groups, there is a well known Mackey irreducibility criteria test for an induced representation to be irreducible (Serre- Linear Representations of Finite Groups - #7.4). The author has stated it for field $\mathbb{C}$. Can we replace $\mathbb{C}$ by Is it true for representations over arbitrary field whose characteristic is zero or co-prime to the order of group ? |
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Mackey Irreducibility CriteriaIn representation theory of finite groups, there is a well known Mackey irreducibility criteria for an induced representation to be irreducible (Serre- Linear Representations of Finite Groups - #7.4). The author has stated it for field $\mathbb{C}$. Can we replace $\mathbb{C}$ by arbitrary field whose characteristic is zero or co-prime to the order of group ?
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