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The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions called k-double Schur functions and affine double Schur functions.
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T. Lam, Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras. Bulletin of the London Math. Soc., to appear
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T. Lam and M. Shimozono, Equivariant affine Pieri rules, in preparation
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T. Lam and M. Shimozono. Quantum cohomology of G / P G/P and homology of affine Grassmannian. Acta Math. 204
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