Geodesic
On the natural representation of the symmetric groups
Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 121-136

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Let E be an arbitrary (non-empty) set and S the restricted symmetric group on E, that is the group of all permutations of E which keep all but a finite number of elements of E fixed. If Φ is any commutative ring with unit element, let Γ = Φ(S) be the group algebra of S over Φ,Γ ⊃ Φ and let M be the free Φ-module having E as Φ-base. The “natural” representation of S is obtained by turning M into a Γ-module in the obvious manner, namely by writing for α∈S, λ1∈Φ, 
Farahat, H. K. On the natural representation of the symmetric groups. Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 121-136. doi: 10.1017/S2040618500034468
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