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Representation theory of the symmetric group

Tensor identity for an induced character

For the standard inclusions $S_2,S_3\leq S_4$,
$$
\left(S^{(2)}\!\uparrow_{S_2}^{S_4}\right)
\otimes
\left(S^{(1^3)}\!\uparrow_{S_3}^{S_4}\right)
\cong S^{(4)}\oplus5S^{(3,1)}\oplus4S^{(2,2)}\oplus7S^{(2,1,1)}\oplus3S^{(1^4)}.
$$


Induced-tensor decomposition for the symmetric group on four points

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 160 / 2 / b / Solution

Induced-tensor decomposition for the symmetric group on four points

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Induced-tensor decomposition for the symmetric group on four points

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