We prove that the representation ring of the symmetric group on $n$ letters is generated by the exterior powers of its natural $(n-1)$-dimensional representation. The proof we give illustrates a strikingly simple formula due to Y. Dvir. We provide an application and investigate a possible generalization of this result to some other reflection groups.
Vertices of Specht modules and blocks of the symmetric group
Character values and decomposition matrices of symmetric groups
A note on the Grothendieck ring of the symmetric group
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