Hello Bruno,
Good advice already on adding the rug. You should consider adding a couple of bookcases (with books in them), perhaps on the side and/or rear walls to break up but not totally absorb reflections.
You want to achieve a mix of both absorbant and reflective surfaces.
Even better advice Alan! You seem to know a lot about sound or something...
The books and bookcase idea is a well known recording studio trick. Placed behind the mixing position, it really helps break up standing waves. I just worked on a project at a studio here in Atlanta that used books on bookshelves in lieu of acoustic treatments (except for bass traps on the ceiling) to great effect. Big tomes of varying sizes work the best.
The hardwood floor problem is one of the reasons I still have carpet in my living room. My 20 foot high angled ceilings with hardwoods would bounce the sound around like crazy. As much as I love hardwood floors as an aesthetic, dust friendly option, good sound comes first!
I just made sure to get really expensive and nice carpet. And like our brothers and sisters of the east, NO. SHOES. INSIDE. EVER.
And not having kids/pets help too...
