For $S_n,$ one can construct all the irreducible representations through the young diagrams. Is there any natural construction for the irreducible representation of $G\wr S_n$ (G is a finite group)?
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3$\begingroup$ It depends what you mean by natural. In Theorem 4.3.34 of James and Kerber's book "The Representation Theory of the Symmetric Group" a complete list of irreducible representations is obtained via Clifford theory. However this is probably not what you're looking for. $\endgroup$– Jay TaylorCommented Jul 29, 2013 at 6:50
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$\begingroup$ @Munees: Besides the older symmetric group literature, the more recent work on rational Cherednik algebras might be suggestive. But as Jay points out, it depends on what is meant by "natural". $\endgroup$– Jim HumphreysCommented Jul 29, 2013 at 14:01
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$\begingroup$ @munees: you might also see this previous post: mathoverflow.net/questions/25625/… $\endgroup$– Ben BraunCommented Jul 30, 2013 at 15:40
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