i second the use of Widget Logic. It is by far the easiest, least-code-involved solution. another option would be to modify the function that displays the sidebars in question so that they have an extra condition.
this first function points the widget area to your new function:
function change_widgetized_area($content) {
$content['1st Subsidiary Aside']['function']='child_1st_subsidiary_aside';
return $content;
}
add_filter('thematic_widgetized_areas', 'change_widgetized_area');
this function is basically the same as thematic_1st_subsidiary_aside() (found in widget-extensions.php) but with an extra condition for is_home():
// Re-Define the 1st Subsidiary Aside
function child_1st_subsidiary_aside() {
if (is_active_sidebar('1st-subsidiary-aside') AND is_home() ) {
echo thematic_before_widget_area('1st-subsidiary-aside');
dynamic_sidebar('1st-subsidiary-aside');
echo thematic_after_widget_area('1st-subsidiary-aside');
}
}