How should I treat window behind listening chair?

Brick it up!
Seriously: I think it's nonsense to hunt for the "ideal room" because there is no such thing. In every concert hall there are hundreds if not thousands of "compromize-spots" to sit in. Who would like to sit in the same seat for a - let's say- guitar recital and an orchestra concert, for a William Byrd mass and Orffs Carmina Burana, for a jazz big band and a choral concert?? I doubt that your window - while probably slightly changing the sound in your room - is doing any bad effect to your LISTENING TO MUSIC which means that any damping will only CHANGE the sound but won't improve your enjoyment of the music!
Relax and enjoy - or call in the brickie.

I put a comforter behind my speakers over the window and it made a huge improvement. Don't worry about absorbing some sound. It is necessary to get clear imaging and kill brightness.

I use wooden venetian blinds on the windows behind my listening chair. Seems to work well for me.

Thank you all for the excellent ideas. I will experiment with them until I find the ideal solution.