Crystal bases : representations and combinatorics
Material type:
TextPublication details: New Jersey : World Scientific, 2017 Description: xii, 279 pages : illustrations ; 26 cmISBN: 9789814733441Subject(s): Lie algebras | Quantum groups | Combinatorial analysisDDC classification: 512.81 Online resources: Table of content | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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NISER LIBRARY | 512.81 BUM-C (Browse shelf(Opens below)) | Available | 25536 |
Includes bibliographical references (pages 263-273) and index.
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.
Graduate students and researchers interested in understanding from a viewpoint of combinatorics on crystal base theory.
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