Does anyone have a reference for a good description of representations of $S\_{n}$ obtained by inducing up from $C\_{S\_{n}}(\pi)$, for some element $\pi$ of $S\_{n}$? (I'd prefer an efficient combinatorial description if there is one.)


This seems like it should be doable, since I'm fairly sure that centralizers of elements are just going to be products (direct and/or wreath) of cyclic groups and smaller symmetric groups, so those representations should all be understandable combinatorially. Any references that people have would be great.


Edit: There are references for inducing from cyclic subgroups, as given in the answer to [Decomposition of induced representations in S\_n](https://mathoverflow.net/questions/54788/decomposition-of-induced-representations-in-s-n?rq=1), and also Stembridge here: <http://www.ams.org/mathscinet-getitem?mr=1023791>, but I'm looking a bit more general than that.



Representations of S_n induced from centralizers of elements
I gave an answer for inducing the trivial representation in a comment at [Decomposing the conjugacy representation of Sym$(n)$ for small $n$](https://mathoverflow.net/questions/153991). It is in terms of a plethysm that seems to be just as intractable as the notorious $s\_m[s\_n]$.


