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 tropical flags and the totally nonnegative flag D ressian
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The coarsest hyperplane subdivisions of the permutahedron into Bruhat interval polytopes from lattice path matroid flags are the only such subdivisions and arise from points in the complete nonnegative flag variety.
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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.
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On subdivisions of the permutahedron and flags of lattice path matroids
The coarsest hyperplane subdivisions of the permutahedron into Bruhat interval polytopes from lattice path matroid flags are the only such subdivisions and arise from points in the complete nonnegative flag variety.