The Tropical Symplectic Grassmannian

RWTH Publications (RWTH Aachen)

Abstract

Abstract We launch the study of the tropicalization of the symplectic Grassmannian, that is, the space of all linear subspaces isotropic with respect to a fixed symplectic form. We formulate tropical analogues of several equivalent characterizations of the symplectic Grassmannian and determine all implications between them. In the process, we show that the Plücker and symplectic relations form a tropical basis if and only if the rank is at most 2. We provide plenty of examples that show that several features of the symplectic Grassmannian do not hold after tropicalizing. We show exactly when do conormal fans of matroids satisfy these characterizations, as well as doing the same for a valuated generalization. Finally, we propose several directions to extend the study of the tropical symplectic Grassmannian.

Authors 1

1. Jorge Alberto Olarte corresponding

   Technische Universität Berlin

   Affiliation as printed

   Institut für Mathematik, Technische Universität Berlin , Straße des 17. Juni 135, 10623 Berlin, Germany