Hooks generate the representation ring of the symmetric group

Details Hooks generate the representation ring of the symmetric group Hooks generate the representation ring of the symmetric group

2011-12-14

arxiv.org/abs/1112.3127v1

Mathematics

Representation Theory

9 pages

Scientific paper

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.

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