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

k-Schur Functions and Affine Schubert Calculus

Mitarbeit:Lam, Thomas; Lapointe, Luc; Morse, Jennifer; Schilling, Anne; Shimozono, Mark; Zabrocki, Mike

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Fields Institute Monographs 33
• Verlag: Springer / Springer New York / Springer, Berlin / The Fields Institute for Research in Mathematical
• Artikelnr. des Verlages: 978-1-4939-4972-4
• Softcover reprint of the original 1st ed. 2014
• Seitenzahl: 228
• Erscheinungstermin: 3. September 2016
• Englisch
• Abmessung: 235mm x 155mm x 13mm
• Gewicht: 367g
• ISBN-13: 9781493949724
• ISBN-10: 1493949721
• Artikelnr.: 45645423

Inhaltsangabe

1. Introduction.- 2. Primer on k-Schur Functions.- 3. Stanley symmetric functions and Peterson algebras.- 4. Affine Schubert calculus.

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1. Introduction.- 2. Primer on k-Schur Functions.- 3. Stanley symmetric functions and Peterson algebras.- 4. Affine Schubert calculus.

Rezensionen

"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)