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Jim Humphreys
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This is by now an old question, but a more recent example is given in a preprint by a current MIT graduate student here. I think the moral of the story is that there are quite a few directions in Lie theory where folding plays a significant role in getting from the simply-laced case to other cases.

Jim Humphreys
  • 52.9k
  • 4
  • 120
  • 241