On representations of the infinite symmetric group

Infinite-dimensional Group Representations

Closed subgroups of the infinite symmetric group

Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪U 〉 = 〈G2 ∪U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on which ...

The Representations of the Symmetric Group

In this paper we classify the irreducible representations of the symmetric group Sn and give a proof of the hook formula for the dimension of each irreducible. 1. The Irreducible Representations of Sn We construct the irreducible representations of the symmetric group. The number of irreducible representations of Sn is the number of conjugacy classes of Sn, which is the number of partitions of ...

On the Modular Representations of the Symmetric Group (II).

On the Modular Representations of the Symmetric Group (III).

In a previous paper2 the author commented upon an idea of D. E. Littlewood' for defining the indecomposables of the regular representation of Sn, and showed how it could be utilized to characterize the modular irreducible components. A modification of Littlewood's idea is presented here which throws new light upon the whole problem. Young's rule3 for constructing the "seminormal" representation...