There is a much more general story here, though one my brain is not very up to explaining it this afternoon, and unfortunately, I don't know of anywhere it's summarized well for beginners.

So, how you you prove the restriction rule you mentioned above?  You note that the restriction of a `S_n` rep to an `S_{n-1}` rep has an action of the [Jucys-Murphy][1] element `X_n`which commutes with `S_{n-1}`.  The different `S_{n-1}` representations are the different eigenspaces of the J-M element.

[1]:http://en.wikipedia.org/wiki/Jucys%E2%80%93Murphy_element

So, one can think of "restrict and take the m-eigenspace" as a functor `E_m`; this defines a direct sum decomposition of the functor of restriction.

Of course, this functor has an adjoint: I think the best way to think about this is as ![F\_m=(k[S\_n]/(X\_n-m))
\otimes\_{k[S\_{n-1}]} V](http://latex.mathoverflow.net/png?F%5Fm%3D%28k%5BS%5Fn%5D%2F%28X%5Fn%2Dm%29%29%0A%5Cotimes%5F%7Bk%5BS%5F%7Bn%2D1%7D%5D%7D%20V).

These functors `E_m,F_m` satsify the relations of the Serre relations for  ![\mathfrak{sl}(\infty)](http://latex.mathoverflow.net/png?%5Cmathfrak%7Bsl%7D%28%5Cinfty%29). Over characteristic 0, these are all different, and you can think of this as an ![\mathfrak{sl}(\infty)](http://latex.mathoverflow.net/png?%5Cmathfrak%7Bsl%7D%28%5Cinfty%29).  If instead, you take representations over characteristic p, ythen `E_m=E_{m+p}` so you can think of them as being in a circle, an affine Dynkin diagram, so one gets an action of ![\widehat{\mathfrak{sl}}(p)](http://latex.mathoverflow.net/png?%5Cwidehat%7B%5Cmathfrak%7Bsl%7D%7D%28p%29).

Similar categorifications of other representations can deconstructed in general by looking at representations of complex reflection groups given by the wreath product of the symmetric group with a cyclic group.  So, Sammy, you shouldn't rescale, you should celebrate that you found a representation with a different highest weight (also, if you really care, you should go talk to Jon Brundan or Sasha Kleshchev; they are some of the world's experts on this stuff).

**EDIT:** Khovanov has actually just posted [a paper](http://arxiv.org/abs/1009.3295) which I think might be relevant to your question.