Hooks generate the representation ring of the symmetric group

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Abstract

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 Dvir. We provide an application and investigate a possible generalization of this result to some other reflection groups. © 2012 Elsevier Ltd.

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Marin, I. (2012). Hooks generate the representation ring of the symmetric group. Expositiones Mathematicae, 30(3), 268–276. https://doi.org/10.1016/j.exmath.2012.03.005

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