Taking Photograph when subject is behind Glass?

Reflections are caused by what the surface "sees" . . . if there is a way of blocking what is exposed to the surface, or forcing the surface to "see" something black or dark, then reflections will be gone.

This is a common technique used by photographers -- using a BLACK card to block reflections from highly reflective surfaces.

HOWEVER ... the situation of your shoot suggests you are far away from the glass booth protecting the Imperial family -- so, you would be unable to use a card, or interfere with the reflections.

In this case, a Polarizing Filter would at least 'help' block reflections -- if your camera could attach filters, and you happened to have a Polarizing Filter on hand.

ANSWER : "NO" there's nothing you can do from a distance, with no filter.

When I create a self-portrait, I will set up my camera on a tripod and have someone pose for me, when I'm happy with what I see we will switch places, then my partner will push down the shutter for me. You could also use the self-timer or a remote if you have one.

A polarising filter will help but you need good light as is reduces light by 1-2 stops

A circular polarizer can help. You'll need to learn to use it (not hard) so get one before it's needed.

http://www.tiffen.com/polarizer_pics.htm