Representation theory of finite symmetric groups

1-dimensional irreps of a finite symmetric group

A symmetric group with has exactly two¹ non-equivalent 1-dimensional irreps rep

• the trivial irrep
• the alternating character

In the Group ring these irreps are carried by left ideäls generated by the Symmetrizer and antisymmetrizer elements.

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Footnotes

1. this is because the Alternating group is the commutator subgroup and therefore is the Abelianization. ↩