Geodesic
Equivariant Pieri rule for the homology of the affine Grassmannian
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 4, pp. 623-648.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: An explicit rule is given for the product of the degree two class with an arbitrary Schubert class in the torus-equivariant homology of the affine Grassmannian. In addition a Pieri rule (the Schubert expansion of the product of a special Schubert class with an arbitrary one) is established for the equivariant homology of the affine Grassmannians of SL $_{ n }$ and a similar formula is conjectured for Sp $_{2n }$ and SO $_{2n+1}$. For SL $_{ n }$ the formula is explicit and positive. By a theorem of Peterson these compute certain products of Schubert classes in the torus-equivariant quantum cohomology of flag varieties. The SL $_{ n }$ Pieri rule is used in our recent definition of k-double Schur functions and affine double Schur functions.
Keywords: Schubert calculus, affine Grassmannian, Pieri rule, quantum cohomology 
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     author = {Lam, Thomas and Shimozono, Mark},
     title = {Equivariant {Pieri} rule for the homology of the affine {Grassmannian}},
     journal = {Journal of Algebraic Combinatorics},
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     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_4_a1/}
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Lam, Thomas; Shimozono, Mark. Equivariant Pieri rule for the homology of the affine Grassmannian. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 4, pp. 623-648. http://geodesic.mathdoc.fr/item/JAC_2012__36_4_a1/