= Column group action
A <column group action> often means the action of a <matrix group> on column <vectors> by left multiplication: $g\cdot v=gv$. The rule $(gh)v=g(hv)$ makes this a left <group action>, and the <identity matrix> fixes every column.
The same term is used in <Young symmetrizers> for the <group> permuting entries within each column of a tableau. In that setting the action permutes labels rather than multiplying a coordinate column. The surrounding representation must specify which meaning is intended. For a concrete coordinate example, a <permutation matrix> exchanges two entries of a column <vector>.
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