Definition
Given a finite symmetric group Sn and specific Young tableau λ corresponding to a numbered partition of n, define two permutation subgroups and of Sn as follows:
and
Corresponding to these two subgroups, define two vectors in the group algebra as
and
where is the unit vector corresponding to g, and is the signature of the permutation. The product
is the Young symmetrizer corresponding to the Young tableau λ. Each Young symmetrizer corresponds to an irreducible representation of the symmetric group, and every irreducible representation can be obtained from a corresponding Young symmetrizer. (If we replace the complex numbers by more general fields the corresponding representations will not be irreducible in general.)
Read more about this topic: Young Symmetrizer
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