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.
By:
Daniel Bump (Stanford Univ Usa), Anne Schilling (Univ Of California, Davis, Usa) Imprint: World Scientific Publishing Co Pte Ltd Country of Publication: Singapore Dimensions:
Height: 241mm,
Width: 168mm,
Spine: 15mm
Weight: 499g ISBN:9789814733441 ISBN 10: 981473344X Pages: 292 Publication Date:18 January 2017 Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format:Paperback Publisher's Status: Active