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Oct 20, 2018 at 10:55 comment added Jason Starr I tried to find counterexamples with solvable subgroups. But then I realized that for a solvable subgroup $B$, the product $B\cdot B$ equals $B$ since it is a subgroup. So the identity is true for $B=B$ a subgroup. Then I tried the simplest one-dimensional subvarieties of the Borel that were actually distinct.
Oct 20, 2018 at 10:50 history answered H A Helfgott CC BY-SA 4.0