That in-line alignment property when I ADD the column doesn't seem to bite. Let me know if this is the way you are doing it. Perhaps the alignment 'assignment' would be needed after the icon assign.
Add the column:
oListView.COLUMNHEADERS.ADD(,"MyColumn1Name","MyColumn1Text",125,,)
Assign the column data alignment:
oListView.COLUMNHEADERS("MyColumn1Name").ALIGNMENT=1
HTH
PS:
Where did you locate the 'triangle images'?