Felipe Rincón
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Isotropical Linear Spaces and Valuated Delta-Matroids
dmtcs:2954 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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https://doi.org/10.46298/dmtcs.2954
Isotropical Linear Spaces and Valuated Delta-MatroidsConference paper
The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n×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.
Michael Joswig;Georg Loho;Dante Luber;Jorge Alberto Olarte, 2022, Generalized Permutahedra and Positive Flag Dressians, International Mathematics Research Notices, 2023, 19, pp. 16748-16777, 10.1093/imrn/rnac349, https://doi.org/10.1093/imrn/rnac349.