On T-invariant subvarieties of symplectic Grassmannians and representability of rank 2 symplectic matroids over C

For the symplectic Grassmannian SpG(2, 2n) of 2-dimensional isotropic subspaces in a 2n-dimensional vector space over an algebraically closed field of characteristic zero endowed with a symplectic form and with the natural action of an n-dimensional torus T on it, we characterize its irreducible T-invariant subvarieties. This characterization is in terms of symplectic Coxeter matroids, and we use this result to give a complete characterization of the symplectic matroids of rank 2 which are representable over C.(c) 2023 Elsevier Inc. All rights reserved.