Isotropical linear spaces and valuated Delta-matroids

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Rincon, Felipe

关键词: Tropical linear space;    Isotropic subspace;    Delta matroid;    Coxeter matroid;    Valuated matroid;    Spinor variety;    Wick relations;    Matroid polytope;    Tropical basis;   

DOI  :  10.1016/j.jcta.2011.08.001

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free