The Tensor Fascia Latae muscles that turn the thighs inwards and open the hips.
The left front and right rear adductor muscles.
The psoas and ilioacus hold the torso vertical and engage to stop you from falling backwards behind the line of gravity which passes behind the hip joints. The psoas, engaged with the rectus abdominis hold you into the centre of the saddle so that your two seat bones are connected to the horse's back muscles on either side of his spine. This is a vital piece of information, for sliding off one side or the other (usually to the outside through corners) is a major cause of horses falling out through their shoulder or haunches or bulging.
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Classical Dressage Notebook