How should I treat window behind listening chair?

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

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

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.

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.

Blackout has less, considerably less absorption coefficient due to the black out foil, however, the foil does create some diffusion. So it's not really a one is better vs the other, it depends on the room and placement.

I have drapes on 3 of the four walls of my listening room because it's a very small room and had annoying slap echo (clap your hands and hear it ring). I find the drapes hugely improve the sound.

However if your system sounds dull and lacking in treble detail the drapes will make it more so, as they affect high frequencies proportionally more.

Marigo Labs makes VTS tuning dots to attach in proximity to corners of windows, as well as other types for every part of a system, and room.
Can check the website, marigoaudio.com
Also, can email Ron Hedrich at the website. He creates the Marigo Labs products.

Rives -

Any chance the BLACKOUT material INSIDE some of the cellular shades helps versus non blackout material shades? Just ordered some and had wondered this.....

Thanks
Dan

Heavy honeycomb cellular shades is a reasonable compromise in many cases.

Well, something is better than nothing. That glass behind you is too reflective. Light drapes might be just the thing. You might run some tests by hanging up light materiel and changing the density incrementally until you get the sound you want. Sheets, blankets etc.

I have a doorwall behind my listening position, and I use two EchoBuster Double Busters in front of it. You're obviously dealing with a window, which is different, but it might be worth contacting EchoBusters and seeing what they offer for that application in terms of diffusion/absorption.