AMS Bookstore LOGO amslogo
AMS TextbooksAMS Applications-related Books
Affine Insertion and Pieri Rules for the Affine Grassmannian
Thomas Lam, Harvard University, Cambridge, MA, Luc Lapointe, Universidad de Talca, Chile, Jennifer Morse, Drexel University, Philadelphia, PA, and Mark Shimozono, Virginia Polytechnic Institute and State University, Blacksburg, VA
cover
SEARCH THIS BOOK:

Memoirs of the American Mathematical Society
2010; 82 pp; softcover
Volume: 208
ISBN-10: 0-8218-4658-2
ISBN-13: 978-0-8218-4658-2
List Price: US$67
Individual Members: US$40.20
Institutional Members: US$53.60
Order Code: MEMO/208/977
[Add Item]

Request Permissions

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.

Table of Contents

  • Schubert bases of \(\mathrm{Gr}\) and symmetric functions
  • Strong tableaux
  • Weak tableaux
  • Affine insertion and affine Pieri
  • The local rule \(\phi_{u,v}\)
  • Reverse local rule
  • Bijectivity
  • Grassmannian elements, cores, and bounded partitions
  • Strong and weak tableaux using cores
  • Affine insertion in terms of cores
  • Bibliography
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia