Title: Totally positive skew-symmetric matrices
Abstract: Skew-symmetric matrices cannot be totally positive in the classical sense (all minors positive). Thus, we define a notion of positivity by viewing them as an affine chart of the orthogonal Grassmannian OGr(n,2n) and considering Lusztig’s positivity in flag varieties. We provide a positivity criterion in terms of a fixed collection of minors, and show that their Pfaffians have a remarkable sign pattern. Finally, we also consider the Euclidean closure of this positive region together with its known CW cell complex structure. We give a way to recognise the cell of a nonnegative point by looking at its underlying matroid.
The talk will be followed by a coffee break.
Date and Venue
Start Date
Venue
FC1 0.29
End Date
Speaker
Veronica Calvo Cortes
Speaker's Institution
Max Planck Institute for Mathematics in the Sciences
Files
Seminario20250325-Calvo_1.pdf494.46 KB
Area
Algebra and Geometry