Assembling Crystals of Type A

Regular An-crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra Uq(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