Equivariant Pieri Rule for the homology of the affine Grassmannian |
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Authors: | Thomas Lam Mark Shimozono |
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Institution: | 1. Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, MI, 48109, USA 2. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0123, USA
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Abstract: | 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. |
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