# Affine Insertion and Pieri Rules for the Affine Grassmannian

ISBN-10: 0821846582

ISBN-13: 9780821846582

Pub. Date: 10/07/2010

Publisher: American Mathematical Society

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

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## Overview

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.

## Product Details

ISBN-13:
9780821846582
Publisher:
American Mathematical Society
Publication date:
10/07/2010
Series:
Memoirs of the American Mathematical Society Series, #208
Pages:
82
Product dimensions:
6.70(w) x 9.90(h) x 0.30(d)

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