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

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

2000-02-14

arxiv.org/abs/math/0002106v1

Mathematics

Combinatorics

7 pages

Scientific paper

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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