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math.CO2026★ 2 cited
Totally Nonnegative Tropical Flags and the Totally Nonnegative Flag Dressian
Jonathan Boretsky
We study the totally nonnegative part of the complete flag variety and of its tropicalization. We show that Lusztig's notion of nonnegative complete flag variety coincides with the…
math.CO2024
Totally positive skew-symmetric matrices
Jonathan Boretsky, Veronica Calvo Cortes, Yassine El Maazouz
A matrix is totally positive if all of its minors are positive. This notion of positivity coincides with the type A version of Lusztig's more general total positivity in reductive…