how to add a class to the widget pager of views slideshow
In fact, after looking at the HTML code generated by views slideshow, pager widget is contained in a div on the same level that the content of the slideshow. So even if I could add a class, it would not be useful because I already positioned text to the right of my image. So the div content of the slideshow is already 100% of the width (and the sub-content have already custom classes to position them in line) .

So I have to use position: absolute to position the pager widget, so I can just add my classes on the container of all global gadgets (positioned at the bottom) by overriding the template views-slideshow.tpl.php as below, and then use the default classes of the widget in my css.

views-slideshow--MY-BANNER.tpl.php 

&lt;div class="skin-&lt;?php print $skin; ?&gt;"&gt;
  &lt;?php if (!empty($top_widget_rendered)): ?&gt;
    &lt;div class="views-slideshow-controls-top clearfix"&gt;
      &lt;?php print $top_widget_rendered; ?&gt;
    &lt;/div&gt;
  &lt;?php endif; ?&gt;

  &lt;?php print $slideshow; ?&gt;

  &lt;?php if (!empty($bottom_widget_rendered)): ?&gt;
    &lt;div class="views-slideshow-controls-bottom MY-CLASSSES clearfix"&gt;
      &lt;?php print $bottom_widget_rendered; ?&gt;
    &lt;/div&gt;
  &lt;?php endif; ?&gt;
&lt;/div&gt;


But I'd like to know if this is possible and with wich function.