Skip to main content
SpringerLink
Log in

k-Schur Functions and Affine Schubert Calculus

  • Book
  • © 2014

Overview

Authors:
  1. Thomas Lam

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Luc Lapointe

    1. Instituto de Matemática y Física, Universidad de Talca, Talca, Chile

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Jennifer Morse

    1. Department of Mathematics, Drexel University, Philadelphia, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  4. Anne Schilling

    1. Department of Mathematics, University of California, Davis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  5. Mark Shimozono

    1. Department of Mathematics, Virginia Tech, Blacksburg, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  6. Mike Zabrocki

    1. Mathematics and Statistics, York University, Toronto, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Fields Institute Monographs (FIM, volume 33)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99 USD 89.00
55% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99 USD 119.99
58% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 59.99 USD 119.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki
    Pages 1-7

  3. Primer on k-Schur Functions

    • Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki
    Pages 9-131

  4. Stanley Symmetric Functions and Peterson Algebras

    • Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki
    Pages 133-168

  5. Affine Schubert Calculus

    • Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki
    Pages 169-212

  6. Back Matter

    Pages 213-219
    Download chapter PDF
Back to top

Keywords

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)

Authors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Thomas Lam

  • Instituto de Matemática y Física, Universidad de Talca, Talca, Chile

    Luc Lapointe

  • Department of Mathematics, Drexel University, Philadelphia, USA

    Jennifer Morse

  • Department of Mathematics, University of California, Davis, USA

    Anne Schilling

  • Department of Mathematics, Virginia Tech, Blacksburg, USA

    Mark Shimozono

  • Mathematics and Statistics, York University, Toronto, Canada

    Mike Zabrocki

Bibliographic Information

  • Book Title: k-Schur Functions and Affine Schubert Calculus

  • Authors: Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki

  • Series Title: Fields Institute Monographs

  • DOI: https://doi.org/10.1007/978-1-4939-0682-6

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2014

  • Hardcover ISBN: 978-1-4939-0681-9Published: 06 June 2014

  • Softcover ISBN: 978-1-4939-4972-4Published: 03 September 2016

  • eBook ISBN: 978-1-4939-0682-6Published: 05 June 2014

  • Series ISSN: 1069-5273

  • Series E-ISSN: 2194-3079

  • Edition Number: 1

  • Number of Pages: VIII, 219

  • Number of Illustrations: 126 b/w illustrations

  • Topics: Combinatorics, Algebraic Geometry, Algebraic Topology

Publish with us

Policies and ethics

Back to top

Search

Navigation