Donggyu Kim (김동규), Grassmann-Plücker functions for orthogonal matroids

We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann-Plücker functions. The equivalence is motivated by Cayley’s identities expressing principal and almost-principal minors of a skew-symmetric matrix in terms of its pfaffians. As a corollary of the new cryptomorphism, we deduce that each component of the orthogonal Grassmannian is parameterized by certain part of the Plücker coordinates.

This is joint work with Changxin Ding.