最終更新日：2022/12/07
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(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 obtained from the action of S_n on V⊗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.
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元となった辞書の項目
Young symmetrizer
noun
(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)
obtained
from
the
action
of
S_n
on
V^(⊗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.
意味（1）
(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)
obtained
from
the
action
of
S_n
on
V^(⊗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.
