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摘要翻译：
研究辛群的仿射Grassmannian Gr的Schubert演算。利用Schur的P和q-函数定义的对称函数的对偶Hopf代数，证明了Gr的积分同调环和上同调环。给出了Gr上同调的Schubert基的显式组合描述，并将其推广到仿射型C Stanley对称函数的定义。对于一类特殊的Schubert类与任意Schubert类的乘积，也给出了一个同调Pieri规则。
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英文标题：
《Schubert Polynomials for the affine Grassmannian of the symplectic group》
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作者：
Thomas Lam, Anne Schilling, Mark Shimozono
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0710.2720
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