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Affine Insertion and Pieri Rules for the Affine Grassmannian

Thomas Lam

出版	American Mathematical Soc., 2010
主題	Mathematics / Discrete MathematicsMathematics / Geometry / GeneralMathematics / Combinatorics
ISBN	08218465829780821846582
URL	http://books.google.com.hk/books?id=CwS6AwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.