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Jun 24, 2012 at 15:06 comment added Jim Humphreys @Mike: As my added comments indicate, your question would be better phrased by substituting "arises in" for "arises as".
Jun 24, 2012 at 13:12 comment added Julien Puydt May I suggest to change the question title for something more explicit?
Jun 24, 2012 at 1:39 vote accept Mike Crumley
Jun 24, 2012 at 0:17 vote accept Mike Crumley
Jun 24, 2012 at 0:17
Jun 23, 2012 at 9:24 comment added Nicola Ciccoli This is no real answer (so I post it as a comment) but as far as 2) may be answered quite generically, if the context is the one of algebraic groups, I found very interesting, though not conclusive for the specific question, the book Algebraic homogeneous spaces and invariant theory by Frank Grosshans, Lect Note Math 1673.
Jun 22, 2012 at 16:44 comment added David E Speyer For reductive connected groups, the only examples I can think of are $G = H \times H'$. Is this the sort of thing you are interested in?
Jun 22, 2012 at 15:42 history edited Jim Humphreys
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Jun 22, 2012 at 15:41 answer added Jim Humphreys timeline score: 6
Jun 21, 2012 at 21:28 history asked Mike Crumley CC BY-SA 3.0