TY  - BOOK
AU  - Lam, Thomas
AU  - Anne Schilling
AU  - Luc Lapointe
AU  - Jennifer Morse
AU  - Mark Shimozono
AU  - Mike Zabrocki
TI  - K-Schur functions and affine Schubert calculus 
T2  - Fields Institute monographs
SN  - 9781493906819 (HB)
PY  - 2014///
CY  - Toronto, New York
PB  - Fields Institute for Research in Mathematical Sciences, Springer
KW  - Schur functions
KW  - Geometry, Algebraic
N1  - Includes bibliographical references (p. 213-219); 1. Introduction -- 2. Primer on k-Schur Functions -- 3. Stanley symmetric functions and Peterson algebras -- 4. Affine Schubert calculus
N2  - 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."--
ER  -