Table of Contents
Algebra
Volume 2013 (2013), Article ID 483949, 14 pages
http://dx.doi.org/10.1155/2013/483949
Research Article

Assembling Crystals of Type A

1Central Institute of Economics and Mathematics, RAS, 47 Nakhimovskii Prospect, Moscow 117418, Russia
2Institute for System Analysis, RAS, 9 Prospect 60 Let Oktyabrya, Moscow 117312, Russia
3Laboratoire J.-V. Poncelet, 11 Bolshoy Vlasyevskiy Pereulok, Moscow 119002, Russia

Received 20 December 2012; Accepted 16 January 2013

Academic Editor: Yao-Zhong Zhang

Copyright © 2013 Vladimir I. Danilov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Regular -crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra . For such a crystal with colors , we consider its maximal connected subcrystals with colors and with colors and characterize the interlacing structure for all pairs of these subcrystals. This enables us to give a recursive description of the combinatorial structure of via subcrystals and develop an efficient procedure of assembling .