Assembling Crystals of Type A. (20th March 2013)

• Record Type: Journal Article
• Authors: Danilov, Vladimir I.; Karzanov, Alexander V.; Koshevoy, Gleb A.
• Other Names: Zhang Yao-Zhong Academic Editor.
• Is Part Of: Algebra. Volume 2013(2013)
• Publication Date: 2013-03-20
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2013/483949
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : Regular A n - crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra U q ( 𝔰 𝔩 n + 1 ) . For such a crystal K with colors 1, 2, …, n, we consider its maximal connected subcrystals with colors 1, …, n - 1 and with colors 2, …, n and characterize the interlacing structure for all pairs of these subcrystals. This enables us to give a recursive description of the combinatorial structure of K via subcrystals and develop an efficient procedure of assembling K .