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

Area

Algebra and Geometry