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＜電子ブック＞
k-Schur Functions and Affine Schubert Calculus / by Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, Mike Zabrocki
(Fields Institute Monographs. ISSN:21943079 ; 33)

版	1st ed. 2014.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	VIII, 219 p. 126 illus : online resource
著者標目	*Lam, Thomas author Lapointe, Luc author Morse, Jennifer author Schilling, Anne author Shimozono, Mark author Zabrocki, Mike author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Algebraic geometry LCSH:Algebraic topology FREE:Discrete Mathematics FREE:Algebraic Geometry FREE:Algebraic Topology
一般注記	1. Introduction -- 2. Primer on k-Schur Functions -- 3. Stanley symmetric functions and Peterson algebras -- 4. Affine Schubert calculus 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-0682-6

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