Group Action of Symmetric Group on Complex Vector Space/Stabilizer/Examples

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Examples of Stabilizers of Group Action of Symmetric Group on Complex Vector Space

Example 1

Let $n = 4$.

Let $v = v_1 + v_2 + v_3 + v_4$.

The stabilizer of $v$ is:

$\Stab v = S_4$


Example 2

Let $n = 4$.

Let $v = v_1 + v_3$.

The stabilizer of $v$ is:

$\Stab v = \set {e, \tuple {1 3}, \tuple {2 4}, \tuple {1 3} \tuple {2 4} }$