Crystal Bases: Representations and Combinatorics - Hardcover

Daniel Bump; Anne Schilling

Hardcover

ISBN 10: 9814733431 ISBN 13: 9789814733434

Publisher: World Scientific Publishing Company, 2017

Synopsis

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.

About this title

From the Back Cover

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 the ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear group, and phenomena in combinatorics. The authors are both contributors to Sage, an open-source mathematical software system, which has strong support for crystal bases and combinatorics and the book takes advantage of this.

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2017
• Language: English
• ISBN 10: 9814733431
• ISBN 13: 9789814733434
• Binding: Hardcover
• Number of pages: 292