Geodesic
A Representation-Theoretic Interpretation of Positroid Classes
Séminaire lotharingien de combinatoire, 78B (2017)

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A positroid variety is the set of points in a complex Grassmannian whose matroid is a fixed positroid, in the sense of Postnikov. A positroid class is then the cohomology class of a positroid variety. We define a family of representations of general linear groups whose characters are the Schur-positive symmetric functions corresponding to positroid classes. This gives a new algebraic interpretation of Schubert times Schur structure coefficients, as well as the three-point Gromov-Witten invariants for Grassmannians, proving a conjecture of Postnikov. As a byproduct we obtain an effective recursion for decomposing positroid classes into Schubert classes. 

@article{SLC_2017_78B_a84,
     author = {Brendan Pawlowski},
     title = {A {Representation-Theoretic} {Interpretation} of {Positroid} {Classes}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a84/}
}
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JO  - Séminaire lotharingien de combinatoire
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PB  - mathdoc
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%0 Journal Article
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%J Séminaire lotharingien de combinatoire
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a84/
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Brendan Pawlowski. A Representation-Theoretic Interpretation of Positroid Classes. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a84/