Noun
Young symmetrizer (plural Young symmetrizers)
(mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space
V
⊗
n
{\displaystyle V^{\otimes n}}
obtained from the action of
S
n
{\displaystyle S_{n}}
on
V
⊗
n
{\displaystyle V^{\otimes n}}
by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers.