Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras

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.

7 pages

References in corpus (2)

• Combinatorial $B_n$-analogues of Schubert polynomials
• Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

Cited by in corpus (7)

• $k$-Schur functions and affine Schubert calculus
• k-shape poset and branching of k-Schur functions
• Stanley symmetric functions and Peterson algebras
• Affine and degenerate affine BMW algebras: The center
• k-Double Schur functions and equivariant (co)homology of the affine Grassmannian
• Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur $P$- and $Q$-functions
• Affine Stanley symmetric functions for classical types