Sound Absorption Behind and Between the Speakers?

Recently my system moved to a new listening room and I was not enjoying the sound very much. There is a window between and behind the speakers. Last night, I put three sound absorbing panels right in front of the window and added a couple salt lamps which illuminate the panels. The sound instantly became way better! I have a soundstage now! I am not sure why though. Do the absorbing panels really have that much of an effect? Or does the fact that I added the panels with the salt lamps give my mind a surface to project the soundstage on which makes a bigger difference? Bit of both?
Every situation is different and I don't have a window behind and between my speakers....but when I experimented with absorption between the speakers it completely killed the soundstage.  Diffusion works much better for me (and I believe many others) between speakers.  Now I do have bass traps in the corners behind the speakers.
The space behind, as well as the floor, is often neglected.  if you have bare floors, try throwing some blankets back there as an experiment.
Same results for me. Absorbion between the speakers provided a focused image but a loss of 3D soundstage, diffusion is more effective. YMMV.
Using foam bass traps helps shape the soundstage and provide depth.

OP, the glass behind your speakers causes reflection of soundwaves. There's no way to produce any sense of

Glass rings. It is also probably acting as an early reflection point for both speakers. Sound from early reflection points is just barely delayed and blurs the overall sound ruining detail and image as you have discovered. If you find the early reflection point on the side walls you can make further improvement. Windows should always be covered. Bulky drapes work great. 
I know this topic gets very complicated, very fast, but why does the space behind and between the speakers make a difference to anything but bass -- if the speakers have forward facing drivers?

First reflection points on side wall, ceiling, floor -- I get why they might mess up soundstage, balance, etc. But behind the speakers -- how does that affect these things?

Your answer will be directly relevant to my situation because I have brick behind and between my speakers. I think it's not *that* pure a reflector but it's not a diffusion panel, either.
It’s a good question! I wonder if flutter echo between the glass and the wall on the opposite side of the room plays a role because you are right: most of the sound (at least at higher frequencies goes forward, not behind the speakers. 
I ended up adding two absorbing panels behind my speakers and it allowed me to fully open the rear port on my sierra raal towers from ascend acoustic. Without the panels I had to use a partial plug that blocked the outer diameter of the port because the bass was overly muddy. It is now a fuller and tighter sound. And I find that diffusers are best at first reflection points on sidewalls and ceiling and on back wall and back sides of side walls. At least in my house of stereo and for my taste. Never made sense to me to have diffusers on front wall behind front facing midrange drivers and tweeters  since diffusers only diffuse higher frequencies.
@hilde45, the reason for treatment on the front wall is to control first reflections and then help on the axial direction.
Absorbtion and Diffraction (either / both) works above 500 Hz.
Bass Trap Placement is at corners and at ceiling / floor / wall intersections.
A lot is happening in the immediate space around a loudspeaker beginning with radiation pattern / edge diffraction / port energy / cabinet /
stand resonance.
Drywall has a relatively high absorption coefficient, foundation walls are well damped but highly reflective. 
Reflections aggregate / accumulate and decay in time domain (waterfall plot).
Look for a balance ...
I once had a fireplace in the middle behind my speakers with glass doors on the enclosure - - it did great damage to the soundstage due to first reflection point issues.  Absorption worked for me then for dedicated listening sessions (but really did not work for my SO!).  Now in a dedicated room I have a wall with GIK panels behind the speakers and I enjoy a deep and expansive sound space.  Maybe deflection would work even better, but I love my art panels - - much more interesting to look at for me!  I also employ absorption at the side wall, ceiling, and floor first reflection points.
@rego and others,

Rego pointed out that:

the reason for treatment on the front wall is to control first reflections and then help on the axial direction.

If the time it takes for the first reflection behind the speakers is longer than the time it takes the sound from front of the speakers to my ears, why would I need to treat them?
Smearing is the term of reference that I see used ... the reflections still have energy ... in a room that is very 'bright' this energy is at higher levels longer.
This is about reinforcement and interference interactions.
The reflections do not stop at the first reflection but go on to two, three and lot more.
These are all ripples at many frequencies in the pond that is the listening space ...
Though the drivers appear as though only front firing, the sound produced is somewhat omnidirectional, especially as frequencies decrease. Typically  speakers are placed so that the wall behind them is closest. The ear/brain mechanism can discriminate between direct and reflected sounds so long as there is about 5 ms between them. If the sound bouncing off the wall behind the speakers (typically the closest wall) is too close, then there isn’t enough time between the direct vs. reflected sound and the sound converges to smear the perceived direct sound. Hence, sound treatment behind and between the speakers.
@rego and @unsound 
That helps. I moved my speakers far enough off the front wall so that there'd be enough of a delay and I wouldn't get the reflected sound *before* the direct sound.

Still, Rego's point is valid. The whole room is still full of energy/information and that can get into the mix, even if it's not interfering, initially, with the direct sound.

That's how I understand what you're saying, at least.
^ For most forward facing driver speakers 3>' from the nearest wall will usually be quite helpful for most users towards ameliorating the time smear of direct vs reflected sound perception. 
In a home audio setting, there is in effect a "competition" between the "small room signature" cues inherent to the playback room, and the "venue cues" which are on the recording, whether the latter be real or engineered or both. The ear/brain system will construct a perception of acoustic space based on the cues which are most plausibly presented to it.

Obviously, we’d like for the recording venue cues to emerge as dominant in this competition.

"Small room signature cues" are strongly conveyed by the earliest reflections, and in particular soundstage depth tends to be limited when there is not much distance between the front wall and the speakers assuming there is a strong reflection off that wall. Three feet was mentioned, and imo that’s a good idea, and ime more is better (though not always practical). The less distance between speakers and the wall behind them, in general the more room for improvement there is in absorbing or diffusing or re-directing that early reflection, even if it’s not very strong because the drivers are front-facing.

The ear/brain system looks at the time delay between the first-arrival sound and the "center of gravity" of reflections in making a judgment about the room size.   If we can manipulate this "center of gravity", we can improve the spatial quality of the playback. 

By taking steps to reduce the magnitude of the earliest reflections, including the one off the wall behind the speakers, we can push that "center of gravity" back in time somewhat, and thereby reduce the degree to which our small room’s signature is superimposed atop the spatial cues on the recording.

In doing so we are "unmasking" the spatial cues on the recording, such that they are not so strongly dominated by the playback room’s acoustic signature. This is imo a worthwhile step towards the suspension of disbelief, and towards that elusive "you are there" presentation.

In practice "you are there" is rare because AT BEST the ear is getting a poverty of venue cues, but if "small room signature cues" have been minimized AND the spatial cues on the recording have been effectively presented (something I haven’t described here), with a good recording it CAN happen.

Nice description of what's going on, Duke!  With the first reflection points well controlled in my room, I am often agog at the "in the venue" feeling I get with many recordings - - seems to transport you to the recording session (which can be a curse with badly done multi-miked recordings!).  Neil Young live at the Roxy is stunning, to name one really good one.
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Thank you very much, jbrrp1 and hilde45. 

Tvad, I’d be inclined to use diffusion rather than absorption, but I’m not expert enough in types of diffusion to make a suggestion beyond that. Phase grating comes to mind as a possibility. If you go with absorption instead, I’d suggest very thick foam (like 4") but covering no more area than necessary.

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Before you jump in sound absorption I suggest that you consider covering the window with materials that will mimic the absorption/reflectivity of the rest of the wall behind the speakers. What you are looking for, ideally, is uniformity across the wall. If you have localized hot spots or reflections you can treat those with spot treatments. 1'x1' diffusers work great for this purpose.

The problem with "absorption" as a universal treatment is that no material "absorbs" sound uniformly, across all frequencies. You may end up with something worse and less treatable. IMO if you stabilize the highly reflective spot between your speakers you will have a uniform, treatable surface that you can tune or use DSP.