Authors:
- 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)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
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.
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Authors and Affiliations
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Department of Mathematics, University of Michigan, Ann Arbor, USA
Thomas Lam
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Instituto de Matemática y Física, Universidad de Talca, Talca, Chile
Luc Lapointe
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Department of Mathematics, Drexel University, Philadelphia, USA
Jennifer Morse
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Department of Mathematics, University of California, Davis, USA
Anne Schilling
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Department of Mathematics, Virginia Tech, Blacksburg, USA
Mark Shimozono
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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