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Induced representations and Mackey theory. (English. Russian original) Zbl 1189.20009

J. Math. Sci., New York 156, No. 1, 11-28 (2009); translation from Sovrem. Mat. Prilozh. 50 (2007).
The authors give an exposition to the theory of induced representations. The notion of induced representation goes back to G. Frobenius and is a powerful tool of constructing representations of groups from those of a subgroup. The authors discuss topics such as induced representations, Frobenius reciprocity law and Mackey’s theory. Finally in the last section of the paper, the authors apply Mackey’s formula to describe a complete list of all the irreducible representations of the symmetric group on \(n\) letters.

MSC:

20C15 Ordinary representations and characters
20C30 Representations of finite symmetric groups
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
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