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A Note on the Symmetric Powers of the Standard Representation of S_n

David Savitt·Richard P. Stanley
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Abstract

In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of the symmetric group S_n is asymptotic to n^2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n^2/2, for this dimension. In particular, for n>6, these characters do not span the full space of class functions on S_n.

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David Savitt, Richard P. Stanley. 2000-02-14. A Note on the Symmetric Powers of the Standard Representation of S_n. https://arxiv.org/abs/math/0002106

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