Last Updated：2025/12/03
Sentence
群代数におけるヤング表に対応する対称化子は冪等元を作り、S_n がテンソル因子を置換して V^{⊗n} に作用することから生じる準同型によるその冪等元の像は複素数体上の対称群の既約表現に対応する。
Quizzes for review
The Young symmetrizer in the group algebra produces an idempotent whose image under the homomorphism induced by S_n acting on V{⊗n} by permuting tensor factors corresponds to an irreducible representation of the symmetric group over the complex numbers.
See correct answer
The Young symmetrizer in the group algebra produces an idempotent whose image under the homomorphism induced by S_n acting on V{⊗n} by permuting tensor factors corresponds to an irreducible representation of the symmetric group over the complex numbers.
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Related words
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.
Japanese Meaning
数学におけるYoung対称化子とは、対称群の群代数の要素として定義され、Sₙがテンソル空間V^(⊗n)の指標の置換によって作用することから得られるエンドモルフィズムとの間の準同型写像により、その像が複素数体上のSₙの既約表現に対応するように構成されたものです。
Related Words
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