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Dec 17, 2013 at 18:07 comment added Jim Humphreys The first version of your question was very narrow, but this one is much too broad. First, you need to clarify what a "nilpotent" element is in the Lie algebra of a real Lie group. Beyond this, the description of centralzers (in the adjoint group) requires much case-by-case study using linear algebra, etc. This depends on classification of (non-compact) real forms of complex Lie algebras and their classes of nilpotents.
Dec 17, 2013 at 11:16 history edited mathuser CC BY-SA 3.0
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Dec 17, 2013 at 11:00 history edited mathuser CC BY-SA 3.0
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Dec 16, 2013 at 21:04 comment added Jim Humphreys It would probably be simplest to contact Ross Lawther and/or Donna Testerman, though Richard Proud did not remain active in mathematical research. (By the way, a UCLA thesis by John Kurtzke in the late 1970s led to a couple of published papers on this theme, but only involving good prime characteristics. My recollection is that there were flaws in his work.)
Dec 16, 2013 at 19:11 history asked mathuser CC BY-SA 3.0