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Let $V$ be a representation with character $\chi$. I would like to have a formula for the characters of the representations $\mathrm{Sym}^m[V]$ and $\wedge ^m[V]$ in terms of $\chi$. Fulton and Harris presents such a formula for $m=2$, but not for general $m$. Is there a "nice" such expression?

I found a paper by Zhou and Pulay, but this doesn't seem to be what I'm looking for (it doesn't seem to give a general formula in terms of $\chi$).

In case the link does not work, here is the reference:

X. Zhou, P. Pulay. Characters for Symmetric and Antisymmetric Higher Powers of Representations: Application to the Number of Anharmonic Force Constants in Symmetrical Molecules. Journal of Computational Chemistry, Vol 10, Issue 7, (1989).

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    X. Zhou, P. Pulay. *Characters for Symmetric and Antisymmetric Higher Powers of Representations: Application to the Number of Anharmonic Force Constants in Symmetrical Molecules*. Journal of Computational Chemistry, Vol 10, Issue 7, (1989).2011-11-21
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    @Srivatsan Is this what you meant by "reference"?2011-11-21
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    http://math.stackexchange.com/questions/39751/how-to-generalise-wedge2-chig-frac12-chig2-chig2/39754#39754 is very similar, and gives a textbook reference2011-11-21

2 Answers 2