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That is an awkward set up! Can you place the speakers and chair elsewhere in the room. I would suggest that finding the best locations is the start, then look at room treatment.
The way you have it in the diagram seems too lopsided for balanced sound from both speakers.
The left speaker is directing sound onto a wall nearer then the right speaker, and also against a nearer back wall. You could try a diagonal arrangement which some have had success with and which I would think could suit your situation. The speakers would be placed either side of the top right corner with your chair roughly where it is now. You should then move the speakers and chair around a bit to get the best, most balanced sound. It takes time to do this but should be worth it. It can help a lot to use a measuring device to do this, but that will add to the learning you need to do. Room EQ Wizard is recommended (there's info on the GIK site about how to use this).After that, listen to GIKs advice.
From what I can gather the top/right corner looks to have a clear floor space of about 18 foot x 20 foot before running into the highlighted corner where the chair is shown. Can you center the system closer into that corner (speakers centered 9 - 10 feet from the corner)? Should be enough space, even with dipoles, oriented either way or as Hipper mentioned on an angle. Best to keep the speakers and the listening position away from walls to minimize room effects. I have an 8ft x 13ft x 21ft room, which is the Cardas Golden Cuboid and the setup is also ala Cardas (roughly 6 foot near-field triangle), but my speakers are traditional (forward facing drivers). I have six GIK 244 panels plus three bookshelves on the side walls, but they offer almost no benefit in this "ideal" situation no matter how I try to orient the panels and the speakers (the GIK panels work miracles elsewhere). The system images really gels in the listening chair.Room impact on sound reproduction is greatly under rated. Treatments aren't cure-alls, better thought of as a band-aid. Recommend reading Floyd Toole's "Sound Reproduction".Speakers should be selected for the given room (space).