Affine Insertion and Pieri Rules for the Affine Grassmannian
Author： Thomas Lam;Luc Lapointe;Jennifer Morse
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405915
P-ISBN(Paperback): 9780821846582
P-ISBN(Hardback): 9780821846582
Subject： O186.13 projective differential geometry
Keyword： Discrete Mathematics and Combinatorics
Language： ENG
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Affine Insertion and Pieri Rules for the Affine Grassmannian
Description
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.