I posted this question on Math SE a month ago but it has had no responses even though I also placed a bounty on it.
Whilst it is at graduate level, I'm unsure whether to ask it here since the question may seem too broad and any answer I get on MO may be too high above my level understanding (I only recently started to learn about algebraic groups).
However, I am still keen on getting some sort of answer to my question, so I would be grateful if you could tell me how to adjust it to make it less broad (eg whether I need to place further hypotheses like reductive etc) and suitable to MO without overcomplicating it.
