Lusztig's surjectivity conjecture for totally positive maximal tori is verified, a new opposition relation on Bruhat intervals is defined and characterized for SL_n, a prior conjecture is disproved, and T>0 is identified as a universal flag amplituhedron.
Totally nonnegative and oscillatory elements in semisimple groups
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Totally nonnegative maximal tori and opposed Bruhat intervals
Lusztig's surjectivity conjecture for totally positive maximal tori is verified, a new opposition relation on Bruhat intervals is defined and characterized for SL_n, a prior conjecture is disproved, and T>0 is identified as a universal flag amplituhedron.