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Schubert polynomials for the affine Grassmannian of the symplectic group

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Abstract

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur’s P and Q functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Thomas Lam

  2. Department of Mathematics, University of California, One Shields Ave, Davis, CA, 95616-8633, USA

    Anne Schilling

  3. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0123, USA

    Mark Shimozono

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  1. Thomas Lam
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  2. Anne Schilling
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  3. Mark Shimozono
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Correspondence to Mark Shimozono.

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Lam, T., Schilling, A. & Shimozono, M. Schubert polynomials for the affine Grassmannian of the symplectic group. Math. Z. 264, 765–811 (2010). https://doi.org/10.1007/s00209-009-0488-9

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  • DOI: https://doi.org/10.1007/s00209-009-0488-9

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