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Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1112/blms/bdq110
arXiv ID: 0906.0385
Source
arXiv
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Abstract

We suggest the point of view that the Schubert classes of the affine Grassmannian of a simple algebraic group should be considered as Schur-positive symmetric functions. In particular, we give a geometric explanation of the Schur positivity of k-Schur functions (at t = 1). We also put this in the context of the theory of combinatorial Hopf algebras.

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