k-Schur Functions and Affine Schubert Calculus (Paperback, Softcover reprint of the original 1st ed. 2014)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Fields Institute Monographs, 33
Release date:	September 2016
First published:	2014
Authors:	Thomas Lam • Luc Lapointe • Jennifer Morse • Anne Schilling • Mark Shimozono • Mike Zabrocki
Dimensions:	235 x 155 x 12mm (L x W x T)
Format:	Paperback
Pages:	219
Edition:	Softcover reprint of the original 1st ed. 2014
ISBN-13:	978-1-4939-4972-4
Categories:	Books > Science & Mathematics > Mathematics > Combinatorics & graph theory Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Topology > Algebraic topology Promotions
LSN:	1-4939-4972-1
Barcode:	9781493949724

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