
k-Schur Functions and Affine Schubert Calculus
Series: Fields Institute Monographs; 33;
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Product details:
- Edition number 2014
- Publisher Springer
- Date of Publication 6 June 2014
- Number of Volumes 1 pieces, Book
- ISBN 9781493906819
- Binding Hardback
- No. of pages219 pages
- Size 235x155 mm
- Weight 4675 g
- Language English
- Illustrations 126 Illustrations, black & white 0
Categories
Short description:
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.
MoreLong description:
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.
?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) More
Table of Contents:
1. Introduction.- 2. Primer on k-Schur Functions.- 3. Stanley symmetric functions and Peterson algebras.- 4. Affine Schubert calculus.
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