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

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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.
7 pages

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Combinatorics, Representation Theory, 05E10

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http://salesiana.dossiersoluciones.com/handle/123456789/58682

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0002106
 http://arxiv.org/abs/math/0002106

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arXiv