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Apr 10, 2015 at 22:28 comment added Jim Humphreys As Geoff says, Steinberg proved this statement in a much more general context for groups of Lie type, following a long history of developments which he refers to. His paper is here: cms.math.ca/10.4153/CJM-1962-018-0
Apr 10, 2015 at 18:43 comment added Geoff Robinson In Steinberg's case they are explicitly described. One is the longest element of the Weyl group, for example.
Apr 10, 2015 at 18:41 comment added Igor Rivin Are the two elements explicit, as they are in the case of $\mathbb{F}_p?$ (as per my answer?
Apr 10, 2015 at 18:40 history answered Geoff Robinson CC BY-SA 3.0