Isotropical Linear Spaces and Valuated Delta-Matroids

Abstract

The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n x n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize tropical Wick vectors in terms of subdivisions of Delta-matroid polytopes, and we examine to what extent the Wick relations form a tropical basis. Our theory generalizes several results for tropical linear spaces and valuated matroids to the class of Coxeter matroids of type D.

References in corpus (3)

• On spinor varieties and their secants
• Representing tropical linear spaces by circuits
• The 4x4 minors of a 5xn matrix are a tropical basis

Cited by in corpus (10)

• Local tropical linear spaces
• Generalized permutahedra and positive flag Dressians
• The tropical symplectic Grassmannian
• Set of independencies and Tutte polynomial of matroids over a domain
• Probabilistic values for simplicial complexes
• The geometry of geometries: matroid theory, old and new
• Detecting tropical defects of polynomial equations
• Representability of orthogonal matroids over partial fields
• Stiefel tropical linear spaces
• Orthogonal matroids over tracts