Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Karpman Rachel

Total positivity for the Lagrangian Grassmannian
Rachel Karpman  1  
1 : University of Michigan [Ann Arbor]  -  Website
500 Church Street Ann Arbor, MI 48109-1090 -  États-Unis

The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties, just as Young diagrams index Schubert varieties. In addition, Postnikov's boundary measurement map gives a family of parametrizations for each positroid variety. The domain of each parametrization is the space of edge weights of a weighted planar network. The positroid stratification of the Grassmannian provides an elementary example of Lusztig's theory of total nonnegativity for partial flag varieties, and has remarkable applications to particle physics. We generalize the combinatorics of positroid varieties to the Lagrangian Grassmannian, the moduli space of maximal isotropic subspaces with respect to a symplectic form. 

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