The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${/rm Gr}$ associated with $SL(n, /mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({/rm Gr})$ and $H_*({/rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({/rm Gr})$. A combinatorial interpretation of the pairing $H^*({/rm Gr})/times H_*({/rm Gr}) /rightarrow/mathbb Z$ induced by the cap product.
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格式 PDF ● 网页 82 ● ISBN 9781470405915 ● 出版者 American Mathematical Society ● 下载 3 时 ● 货币 EUR ● ID 6613164 ● 复制保护 Adobe DRM
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