A Note on the Symmetric Powers of the Standard Representation of S_n
Combinatorics
2007-05-23 v1 Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0002106,
title = {A Note on the Symmetric Powers of the Standard Representation of S_n},
author = {David Savitt and Richard P. Stanley},
journal= {arXiv preprint arXiv:math/0002106},
year = {2007}
}
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7 pages