Schubert Polynomials for the affine Grassmannian of the symplectic group

Details Schubert Polynomials for the affine Grassmannian of the symplectic group Schubert Polynomials for the affine Grassmannian of the symplectic group

2007-10-15

arxiv.org/abs/0710.2720v2

Mathematische Zeitschrift 264(4) (2010) 765-811

Mathematics

Combinatorics

45 pages

Scientific paper

10.1007/s00209-009-0488-9

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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