TY  - BOOK
AU  - Bump,Daniel
AU  - Schilling,Anne
TI  - Crystal bases: representations and combinatorics 
SN  - 9789814733441
U1  - 512.81 
PY  - 2017///
CY  - New Jersey
PB  - World Scientific
KW  - Lie algebras
KW  - Quantum groups
KW  - Combinatorial analysis
N1  - Includes bibliographical references (pages 263-273) and index; Graduate students and researchers interested in understanding from a viewpoint of combinatorics on crystal base theory
N2  - This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained
UR  - https://www.worldscientific.com/doi/reader/10.1142/9789814733458_fmatter
UR  - https://www.goodreads.com/book/show/28350083-crystal-bases#CommunityReviews
ER  -