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Zbl 0695.20008
Inglis, N.F.J.; Richardson, R.W.; Saxl, J.
An explicit model for the complex representations of $S\sb n$.
(English)
[J] Arch. Math. 54, No.3, 258-259 (1990). ISSN 0003-889X; ISSN 1420-8938/e

The authors provide the following elegant construction of the model character (the sum of all the irreducibles) for the symmetric group, in terms of plethysms and using the Littlewood-Richardson rule: $$\sum\sb{\alpha \vdash n}[\alpha]=\sum\sb{0\le k\le n/2}([2]\odot [k])[1\sp{n-2k}].$$
[A.Kerber]
MSC 2000:
*20C30 Representations of finite symmetric groups

Keywords: model character; symmetric group; plethysms; Littlewood-Richardson rule

Cited in: Zbl 0674.20005

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