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  1. Home > Articles & Issues >
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Conference paper

Total positivity for the Lagrangian Grassmannian

Rachel Karpman ORCID (1) (2)
(1) University of Michigan [Ann Arbor]
(2) Université du Michigan = University of Michigan [Ann Arbor]
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Imported on
July 4, 2016
Published on
April 22, 2020
Last modified on
March 31, 2025
Volume
DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
DOI
10.46298/dmtcs.6392
License
https://about.hal.science/hal-authorisation-v1
EMSW21-RTG: Developing American Research Leadership in Algebraic Geometry and its Boundaries
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Total positivity for the Lagrangian Grassmannian

Rachel Karpman ORCID (1) (2)
(1) University of Michigan [Ann Arbor]
(2) Université du Michigan = University of Michigan [Ann Arbor]
Abstract
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 non negativity 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
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
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