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Oct 3, 2017 at 12:46 comment added bob Hey, thanks for your comments. Yeah I think that if $H \cap H'$ is trivial then my description gives way to many representations. So it's definitely not the right answer. But I was wondering if someone knows the right one :)
Oct 3, 2017 at 11:25 comment added Tobias Kildetoft As indicated by @SimonWadsley finite groups is a good place to start to see what is going on, and why this is not the right answer. For example if you take $G = S_3$ and subgroups of order $2$ and $3$ then your description would give way too many representations.
Oct 3, 2017 at 9:10 comment added Simon Wadsley I think that consideration of finite groups (which can be viewed as algebraic groups of course) might help you assess whether anything like this is at all plausible.
Oct 3, 2017 at 7:42 history edited Paul Broussous
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Oct 2, 2017 at 22:53 history asked bob CC BY-SA 3.0