Séminaire Lotharingien de Combinatoire, 78B.85 (2017), 12 pp.

Brendan Pawlowski

A Representation-Theoretic Interpretation of Positroid Classes

Abstract. 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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