  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.
