Fields Institute Monographs

k-Schur Functions and Affine Schubert Calculus

Authors: Lam, Th., Lapointe, L., Morse, J., Schilling, A., Shimozono, M., Zabrocki, M.

  • Summarizes the current state in an active area of research and outlines the open research questions which motivate the subject
  • Demonstrates calculations using the software package Sage so that readers can more easily experiment and develop conjectures themselves
  • Contains examples and exercises, among other introductory material, to assist advanced undergraduates and graduate students in getting started in the area
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eBook $79.99
price for USA (gross)
  • ISBN 978-1-4939-0682-6
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  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-1-4939-0681-9
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  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-1-4939-4972-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry.

This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.

Reviews

“The monograph under review provides a nice introduction to the theory of k-Schur functions and affine Schubert calculus over the last ten years. … this is an invaluable research monograph. I highly recommend it to anyone who wants to enter this fascinating new field.” (Arthur L. B. Yang, Mathematical Reviews, February, 2017)


Table of contents (4 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-1-4939-0682-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-1-4939-0681-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-1-4939-4972-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
k-Schur Functions and Affine Schubert Calculus
Authors
Series Title
Fields Institute Monographs
Series Volume
33
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4939-0682-6
DOI
10.1007/978-1-4939-0682-6
Hardcover ISBN
978-1-4939-0681-9
Softcover ISBN
978-1-4939-4972-4
Series ISSN
1069-5273
Edition Number
1
Number of Pages
VIII, 219
Number of Illustrations and Tables
126 b/w illustrations
Topics