Isotropical linear spaces and valuated Delta-matroids

Authors:
Felipe Rincón
Affiliations:
University of California, Berkeley, Department of Mathematics, 1045 Evans Hall, Berkeley, CA, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2012

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Abstract

The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an nxn 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 @D-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.