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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…
math.CO2024
On two notions of total positivity for generalized partial flag varieties of classical Lie types
Grant Barkley, Jonathan Boretsky, Christopher Eur +1
For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory…