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