Séminaire Lotharingien de Combinatoire, 78B.85 (2017), 12 pp.
A Representation-Theoretic Interpretation of Positroid Classes
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.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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